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Lesson Practice 1a - sYsteMatic reVieW 1c 155aLGeBra 1
Lesson Practice 1A1.
2.
3.
4
5.
done
done
6 5 30
8 5 40
8 6 6 8
( ) −( ) = −−( ) −( ) =+ = +
.
114 14
5 9 9 545
=( )
× = ×
truecommutative property
6.
=
( )
− = −= −
45
8 4 4 84
truecommutative property
7.44
36 4 4 36
9 436
19
2 9 8 2
false
or false
8.
9.
÷ ÷=
=
+( ) + = ++ +( )= +=
9 8
11 8 2 1719 19
+
true
associative
property( )
×( ) × = × ×( )× = ×
=
10. 4 5 6 4 5 6
20 6 4 30120 120 ttrue
associative property ( )
−( ) − = − −(11. 11 4 2 11 4 2))− = −
( ) = ( )=
7 2 11 2
5 9
9 3 3 9 3 3
3 3 9 1
1 9
≠
÷ ÷ ÷ ÷
÷ ÷
≠
false
12.
false
false see
true see
true
13.
14.
15.
; #
; #
;
7
9
ssee and # #6 10
Lesson Practice 1BLessonPractice1B1.
2.
−( )+ −( )=−−( ) − +( ) =3 10 13
3 10 −−( ) + −( ) = −( ) − −( ) = ( ) + +( ) =−( ) − −(
3 10 13
6 5 6 5 11
8 5
3.
4. )) = −( ) + +( ) = −
− + − + =+ − − + = −
8 5 3
5 6 8 35 8 6 3
5. D C D C BD D C C B B 99 13
2 32 3 4
5 3 4
C D
A B A BA A B B A B
Q C C Q Q
+
+ − + =− + + = +
+ − + +
6.
7. −− =+ + + − − = − +
+ − + + + −
5
5 4 3 5 3 10
20 5 6 2 9
C
Q Q Q C C C C Q
X Y Y X X8. ==− + + + − + = − +
+ − + =− +
20 9 5 2 6 8 5 11
2 2 22 2
X X X Y Y X Y
X X XX X X
9.++ = +
− + − − =+ − − − = −
−
2 3 2
3 1 2 1 43 2 4 1 1 2
5 6
X
Y Y YY Y Y Y
A
10.
11. BB B AA A B B A B
X Y X
− + − =+ − − − = − −
− −
3 10 85 10 6 3 8 15 9 8
18 5 9
1.
2.
−( )+ −( )=−−( ) − +( ) =3 10 13
3 10 −−( ) + −( ) = −( ) − −( ) = ( ) + +( ) =−( ) − −(
3 10 13
6 5 6 5 11
8 5
3.
4. )) = −( ) + +( ) = −
− + − + =+ − − + = −
8 5 3
5 6 8 35 8 6 3
5. D C D C BD D C C B B 99 13
2 32 3 4
5 3 4
C D
A B A BA A B B A B
Q C C Q Q
+
+ − + =− + + = +
+ − + +
6.
7. −− =+ + + − − = − +
+ − + + + −
5
5 4 3 5 3 10
20 5 6 2 9
C
Q Q Q C C C C Q
X Y Y X X8. ==− + + + − + = − +
+ − + =− +
20 9 5 2 6 8 5 11
2 2 22 2
X X X Y Y X Y
X X XX X X
9.++ = +
− + − − =+ − − − = −
−
2 3 2
3 1 2 1 43 2 4 1 1 2
5 6
X
Y Y YY Y Y Y
A
10.
11. BB B AA A B B A B
X Y X
− + − =+ − − − = − −
− −
3 10 85 10 6 3 8 15 9 8
18 5 912. ++ =− − + = −
YX X Y Y X Y
false
tru
18 9 5 9 4
13.
14.
; see 1A #12
ee
false
;
;
see 1A #6
see 1A #1115.
Systematic Review 1C1.
2.
4 2 2 2 3
4 2 2 2 3 3 2
5 7 3
Q C C Q C
Q Q C C C C Q
M
+ − − − =− + − − = − +
− − + MMM M M
A B C A B CA A
− + =− + − − + = − −
− + − + + =− −
4 55 3 7 4 5 2 6
2 3 42
3.33 4 2 5
4 5 2 7 14 2 5 7 1 2
B B C C A B C
A AA A A
+ + + = − +
− − + − =− − + − = +
4.11
4 3 6 10 54 10 3 6 5 14 9 5
15
5.
6.
X Y Y XX X Y Y X Y
X
− − + − =+ − − − = − −
−− − + =− − + = −
+ − − − +
4 615 6 4 9 3
15 6 4 5 14 1
Y X YX X Y Y X Y
X X Y Y X7. 0015 6 14 4 5 10 7 9 10
3 4 6 7 8
=+ − − − + = − +
− + + + =
X X X Y Y X Y
A B A B8.33 6 4 7 8 9 3 8
3 5 15
81 9
A A B B A B+ − + + = + +
−( )( ) = −
−( ) −(9.
10. ÷ )) =−( ) = −
−( ) = −( ) −( ) =+ −( ) =
9
4 2 2
5 5 5 25
4 2 4
2
11.
12.
13.
÷
−− =
− = − ×( ) = −
× × =
× ×
2 2
4 4 4 16
14
711
47
111
12
56
1
14.
15.
16. 1112
55144
13
45
515
1215
5 1215 15
5 121
512
=
= = = =17. ÷ ÷ ÷÷
÷
Student Solutions Σ5 3Σ5 3 4Σ4QΣQ5 3Q5 3Σ5 3Q5 3C C QΣC C Q QΣQ+ −Σ+ −5 3+ −5 3Σ5 3+ −5 3C C Q+ −C C QΣC C Q+ −C C Q+ +Σ+ +C C Q+ +C C QΣC C Q+ +C C Q7.Σ7. − =Σ− =−− =−Σ−− =−− =Σ− = − +Σ− +
+ −Σ+ − + +Σ+ +
5Σ5− =5− =Σ− =5− =5 4Σ5 4+ +5 4+ +Σ+ +5 4+ + 3 5Σ3 5+ −3 5+ −Σ+ −3 5+ − 3 1Σ3 1− +3 1− +Σ− +3 1− +
20Σ20 5 6Σ5 6+ −5 6+ −Σ+ −5 6+ − 2 9Σ2 9+ −2 9+ −Σ+ −2 9+ −
CΣC− =C− =Σ− =C− =Q QΣQ Q5 4Q Q5 4Σ5 4Q Q5 4+ +5 4+ +Q Q+ +5 4+ +Σ+ +5 4+ +Q Q+ +5 4+ + Q CΣQ C+ −Q C+ −Σ+ −Q C+ −3 5Q C3 5Σ3 5Q C3 5+ −3 5+ −Q C+ −3 5+ −Σ+ −3 5+ −Q C+ −3 5+ − C CΣC C− =C C− =Σ− =C C− =3 5C C3 5Σ3 5C C3 5− =3 5− =C C− =3 5− =Σ− =3 5− =C C− =3 5− = C QΣC Q3 1C Q3 1Σ3 1C Q3 1− +3 1− +C Q− +3 1− +Σ− +3 1− +C Q− +3 1− +
X YΣX Y5 6X Y5 6Σ5 6X Y5 6+ −5 6+ −X Y+ −5 6+ −Σ+ −5 6+ −X Y+ −5 6+ − Y XΣY X+ +Y X+ +Σ+ +Y X+ +2 9Y X2 9Σ2 9Y X2 92 9X2 9Σ2 9X2 9+ −2 9+ −X+ −2 9+ −Σ+ −2 9+ −X+ −2 9+ −8.Σ8. ===Σ===− +Σ− + − +Σ− +
+ =Σ+ =
20Σ20 9 5Σ9 5− +9 5− +Σ− +9 5− + 2 6Σ2 6+ +2 6+ +Σ+ +2 6+ + 8 5 1Σ8 5 1
2 2Σ2 2 2Σ2+ =2+ =Σ+ =2+ =
X XΣX X+ +X X+ +Σ+ +X X+ +2 6X X2 6Σ2 6X X2 6+ +2 6+ +X X+ +2 6+ +Σ+ +2 6+ +X X+ +2 6+ + X YΣX Y− +X Y− +Σ− +X Y− +2 6X Y2 6Σ2 6X Y2 6− +2 6− +X Y− +2 6− +Σ− +2 6− +X Y− +2 6− + Y XΣY X= −Y X= −Σ= −Y X= −8 5 1Y X8 5 1Σ8 5 1Y X8 5 1= −8 5 1= −Y X= −8 5 1= −Σ= −8 5 1= −Y X= −8 5 1= −
X XΣX X+ −X X+ −Σ+ −X X+ −2 2X X2 2Σ2 2X X2 2+ −2 2+ −X X+ −2 2+ −Σ+ −2 2+ −X X+ −2 2+ − XΣX+ =X+ =Σ+ =X+ =9.Σ9.
Student Solutions ΣStudent Solutions
aLGeBra 1
sYsteMatic reVieW 1c - sYsteMatic reVieW 1D
soLutions156
0015 6 14 4 5 10 7 9 10
3 4 6 7 8
=+ − − − + = − +
− + + + =
X X X Y Y X Y
A B A B8.33 6 4 7 8 9 3 8
3 5 15
81 9
A A B B A B+ − + + = + +
−( )( ) = −
−( ) −(9.
10. ÷ )) =−( ) = −
−( ) = −( ) −( ) =+ −( ) =
9
4 2 2
5 5 5 25
4 2 4
2
11.
12.
13.
÷
−− =
− = − ×( ) = −
× × =
× ×
2 2
4 4 4 16
14
711
47
111
12
56
1
14.
15.
16. 1112
55144
13
45
515
1215
5 1215 15
5 121
512
=
= = = =17. ÷ ÷ ÷÷
÷
118. 7 12
2 47
152
187
10514
3614
105 3614 14
105
÷ ÷ ÷
÷÷
÷
= =
= = 3361
10536
2 3336
2 1112
13
45
13
54
512
7 12
= = =
= × =19.
20.
÷
÷22 47
152
187
152
718
10536
2 3336
2 1112
= = ×
= = =
÷
Systematic Review 1D1.
2.
2 3 4 4 5
2 4 5 3 4
18 5
A B A B A
A A A B B A B
X
− + + − =+ −( ) + − +( ) = +
+ XX Y Y X Y
X X X Y Y Y X
− − − + =+ −( ) + − − +( ) = −
6 8 11 10
18 5 11 6 8 10 12 44
4 4 16 7 18
4 16 4 7 18 20 3
Y
A B A B
A A B B A
3. − + + + =+( ) + − +( ) + = + BB
X X
X X X
K K
+
− + + − =− +( ) + −( ) = −
− + −
18
5 3 8 4
5 8 3 4 3 1
8 6 3
4.
5. 22 3
8 3 2 3 6 9 3
10 3 9 3
10
K
K K K K
C C D D C
C
+ =+ −( ) + −( ) = −
− − + − =6.
−− −( ) + − +( ) = −
− − − =−( )
3 9 3 6 6
13 8 2 12
13 2
C C D D C D
A Z A Z
A A
7.
++ − −( ) = −
− − + + − =− + −
8 12 11 20
7 4 4 5 8 7
7 4 5 7
Z Z A Z
D D D D
D D D
8.
DD D( ) + − +( ) = +
−( ) = −( ) −( ) =− = − ( )( )
4 8 4
3 3 3 9
3 3 3
2
3
9.
10. 33 27
6 2 12
4 3 4 3
( ) = −
−( ) −( ) = +
−( ) − −( ) = −( ) + +( ) = −
11.
12. 11
45
12
58
14
12
67
23
27
58
17
1
1
1
2
1
3
1
1
13.
14.
15.
× × =
× × =
=
= −
− − − =−( )
3 9 3 6 6
13 8 2 12
13 2
C C D D C D
A Z A Z
A A
7.
++ − −( ) = −
− − + + − =− + −
8 12 11 20
7 4 4 5 8 7
7 4 5 7
Z Z A Z
D D D D
D D D
8.
DD D( ) + − +( ) = +
−( ) = −( ) −( ) =− = − ( )( )
4 8 4
3 3 3 9
3 3 3
2
3
9.
10. 33 27
6 2 12
4 3 4 3
( ) = −
−( ) −( ) = +
−( ) − −( ) = −( ) + +( ) = −
11.
12. 11
45
12
58
14
12
67
23
27
58
17
1
1
1
2
1
3
1
1
13.
14.
15.
× × =
× × =
=÷ 33556
856
358
4 38
58
17
58
71
358
4 38
28
2
÷
÷
= =
= × = =16.
17./ \
114
2 7
2 2 7
42
2 21
3 7
2 3 7
48
2 24
2 12
/ \
/ \
/ \
/ \
/ \
/
× ×
× ×18.
19.
\\
/ \
/ \
/ \
/ \
2 6
2 3
2 2 2 2 3
100
2 50
2 25
5 5
2 2 5 5
× × × ×
× × ×
20.
aLGeBra 1
sYsteMatic reVieW 1D - sYsteMatic reVieW 1e
soLutions 157
/ \
114
2 7
2 2 7
42
2 21
3 7
2 3 7
48
2 24
2 12
/ \
/ \
/ \
/ \
/ \
/ \\
/ \
/ \
/ \
/ \
2 6
2 3
2 2 2 2 3
100
2 50
2 25
5 5
2 2 5 5
× × × ×
× × ×
20.
Systematic Review 1ESystematicReview1E1. 1 2 3 1 2 3
1 4
2 2 2 2 2 2+( ) + = + +( )+( )) + = + +( )
+ = +=
( )
9 1 4 9
5 9 1 1314 14
81 9 3
9
2.
3.
yes
÷ ÷ ≠
÷÷ ≠
≠
÷ ÷
÷3
3
81 9 3
81 3
27
3 4 3 4 3 336
( )( )
( )
× × = × ×
4.
5.
no
==
− −−
− −−
−
36
125 15 4110 4
106
15 4 12511 125
11
6.
7.
yes
≠≠≠ 44
14
35
53
14
116
311
47
27
1
1
1
1
1
2
1
1
2
1
8.
9.
10.
11
no
× × =
× × =
..
12.
13.
74
78
5632
2832
5628
2
74
78
74
87
21
1
2
1
÷ ÷
÷
= = =
= × =
116
2 8
2 4
2 2
2 2 2 2
54
2 27
3 9
3 3
2 3 3 3
/ \
/ \
/ \
/ \
/ \
/ \
× × ×
× × ×14.
115.
16.
72
2 36
2 18
2 9
3 3
2 2 2 3 3
36
2 18
2 9
/ \
/ \
/ \
/ \
/ \
/ \
44
14
35
53
14
116
311
47
27
1
1
1
1
1
2
1
1
2
1
8.
9.
10.
11
× × =
× × =
..
12.
13.
74
78
5632
2832
5628
2
74
78
74
87
21
1
2
1
÷ ÷
÷
= = =
= × =
116
2 8
2 4
2 2
2 2 2 2
54
2 27
3 9
3 3
2 3 3 3
/ \
/ \
/ \
/ \
/ \
/ \
× × ×
× × ×14.
115.
16.
72
2 36
2 18
2 9
3 3
2 2 2 3 3
36
2 18
2 9
/ \
/ \
/ \
/ \
/ \
/ \
× × × ×
// \
3 3
2 2 3 3
2436
2 123 12
23
102
× × ×
= ××
=17.
18.
12 is GCF
552 55 5
25
3045
2 153 15
23
= ××
=
= ××
=
5 is GCF
15 is 19. GGCF
8 is GCF20. 3256
4 87 8
47
= ××
=
aLGeBra 1
Lesson Practice 2a - Lesson Practice 2B
soLutions158
Lesson Practice 2ALessonPractice 2A1.
2.
38
38
14
2858
56
=
+ =
LCM is 8
==
− =
=
=
+ =
2530
310
9301630
815
23
1015
45
121
LCM is 30
3.
552215
1 715
5 6 4 5 6 16 30 16 46
9
2
=
⋅ + = ⋅ + = + =
LCM is 15
4.
5. ⋅⋅ − = ⋅ −= − =
⋅ = ⋅ =
4 19 9 16 19144 19 125
6 8 2 36 8 2 288 2
2
26. ÷ ÷ ÷ ==
⋅ + − = ⋅ + − =
+ − = − =
144
12 3 4 8 12 3 16 8
36 16 8 52 8 44
18
27.
8. ÷22 5 6 9 5 6 45 6 51
3 8 3 3 3 8 92 2
⋅ + = ⋅ + = + =
−( ) + +( ) = −( ) −( ) + +9. (( )= + =
+ − = + − =+ − = − =
9 17 26
8 32 4 2 8 32 4 48 8 4 16 4 12
210.
1
÷ ÷
11.
12.
3 3 5 4 7
3 5 3 4 7 8 7
5
A B A B
A A B B A B
− + + + =+( ) + − +( ) + = + +
⋅66 5 36 180 180
18 2 18 8 26 26
3 8 9 6
2
3
2 2
= ⋅ = =
+ = + = =
− = −
13.
14. 44 55 55
4 2 16 4 12 122 2
= − =
− = − = =15.
LessonPractice 2A1.
2.
38
38
14
2858
56
=
+ =
LCM is 8
==
− =
=
=
+ =
2530
310
9301630
815
23
1015
45
121
LCM is 30
3.
552215
1 715
5 6 4 5 6 16 30 16 46
9
2
=
⋅ + = ⋅ + = + =
LCM is 15
4.
5. ⋅⋅ − = ⋅ −= − =
⋅ = ⋅ =
4 19 9 16 19144 19 125
6 8 2 36 8 2 288 2
2
26. ÷ ÷ ÷ ==
⋅ + − = ⋅ + − =
+ − = − =
144
12 3 4 8 12 3 16 8
36 16 8 52 8 44
18
27.
8. ÷22 5 6 9 5 6 45 6 51
3 8 3 3 3 8 92 2
⋅ + = ⋅ + = + =
−( ) + +( ) = −( ) −( ) + +9. (( )= + =
+ − = + − =+ − = − =
9 17 26
8 32 4 2 8 32 4 48 8 4 16 4 12
210.
1
÷ ÷
11.
12.
3 3 5 4 7
3 5 3 4 7 8 7
5
A B A B
A A B B A B
− + + + =+( ) + − +( ) + = + +
⋅66 5 36 180 180
18 2 18 8 26 26
3 8 9 6
2
3
2 2
= ⋅ = =
+ = + = =
− = −
13.
14. 44 55 55
4 2 16 4 12 122 2
= − =
− = − = =15.
Lesson Practice 2BLessonPractice 2B1. 16 2 2 2 2
18 2 3 32 2 2
= × × ×= × ×= × ×LCM ×× × × =
= ×= ×= × × =
= × ×
2 3 3 144
10 2 514 2 7
2 5 7 70
24 2 2 2
2.
3.
LCM
××= × ×= × × × × × =
⋅ + = ⋅( ) + =
350 2 5 5
2 2 2 3 5 5 600
4 8 3 4 8 92
LCM
4. 332 9 41
10 4 25 10 16 25 160 25 135
7 9
2
2
+ =
⋅ − = ⋅( ) − = − =
−
5.
6. ÷22 49 9 2 49 4 5 44 5
18 2 5 11 18 2 25 12
= − ( ) = − =
⋅ + − = ⋅( ) + −
÷ . .
7. 11
36 25 11 50
15 3 8 10 5 8 10 40 10 50
5
= + − =⋅ + = ⋅( ) + = + =
−
8.
9.
÷
(( ) + +( ) = + +( ) = + =
+ − =
2 2
2 3
9 4 25 9 16 25 25 50
9 48 12 3 8110. ÷ ++ ( ) −= + − =
− + ( ) = − + ( )
48 12 27
81 4 27 58
4 9 8 4 4 9 22 2 2 2
÷
÷11.
== − + = + =
− − ( ) + = − − ( ) +
16 9 4 7 4 11
3 5 15 3 18 3 5 5 12 2 3 2 2 312. ÷ 88
9 25 125 18
16 125 18
16 125 18 91
10 52
= − − += − − += − + = −
−13. 22 2
2
8 2 100 25 8 4
75 4 75 4 79
18 36 3 5
+ − + = − + − += + − = + =
− + −14. −−( )= − + − −( )= − + − −( )= + −
15
18 36 3 25 15
18 22 15
18 22 15
2
2
2
(( )= + = + =
−( ) − − − = − − −
2
2
2 4 2
18 7 18 49 67
10 9 2 5 100 9 16 215. 55
91 9 91 9 82= − − = − =
LessonPractice 2B1. 16 2 2 2 2
18 2 3 32 2 2
= × × ×= × ×= × ×LCM ×× × × =
= ×= ×= × × =
= × ×
2 3 3 144
10 2 514 2 7
2 5 7 70
24 2 2 2
2.
3.
LCM
××= × ×= × × × × × =
⋅ + = ⋅( ) + =
350 2 5 5
2 2 2 3 5 5 600
4 8 3 4 8 92
LCM
4. 332 9 41
10 4 25 10 16 25 160 25 135
7 9
2
2
+ =
⋅ − = ⋅( ) − = − =
−
5.
6. ÷22 49 9 2 49 4 5 44 5
18 2 5 11 18 2 25 12
= − ( ) = − =
⋅ + − = ⋅( ) + −
÷ . .
7. 11
36 25 11 50
15 3 8 10 5 8 10 40 10 50
5
= + − =⋅ + = ⋅( ) + = + =
−
8.
9.
÷
(( ) + +( ) = + +( ) = + =
+ − =
2 2
2 3
9 4 25 9 16 25 25 50
9 48 12 3 8110. ÷ ++ ( ) −= + − =
− + ( ) = − + ( )
48 12 27
81 4 27 58
4 9 8 4 4 9 22 2 2 2
÷
÷11.
== − + = + =
− − ( ) + = − − ( ) +
16 9 4 7 4 11
3 5 15 3 18 3 5 5 12 2 3 2 2 312. ÷ 88
9 25 125 18
16 125 18
16 125 18 91
10 52
= − − += − − += − + = −
−13. 22 2
2
8 2 100 25 8 4
75 4 75 4 79
18 36 3 5
+ − + = − + − += + − = + =
− + −14. −−( )= − + − −( )= − + − −( )= + −
15
18 36 3 25 15
18 22 15
18 22 15
2
2
2
(( )= + = + =
−( ) − − − = − − −
2
2
2 4 2
18 7 18 49 67
10 9 2 5 100 9 16 215. 55
91 9 91 9 82= − − = − =
aLGeBra 1
sYsteMatic reVieW 2c - sYsteMatic reVieW 2D
soLutions 159
Systematic Review 2C LessonPractice 2C1.
2.
4 7 3 4 7 9 37
5 8 2 2
2
2
⋅ + = ⋅( ) + =
+ =÷ 55 8 2 25 4 29
12 2 3 4 144 5 4
720 4 716
2
+ = + =
× +( ) − = ×( ) −= − =
÷
3.
44.
5.
6.
9 1 8 9 1 8 9 8 1
14 2 1 6 7 6 1
6 28 7
2× − = ×( ) − = − =− × = − =
+
÷
÷ −− = + − = −
−( ) + = + = + =
−( ) ×
4 6 4 16 6
3 9 6 9 9 6 1 6 7
6 2 5
2
27.
8.
÷ ÷
÷ ++ = − × += × + = + =
× × =
3 3 5 9
3 5 9 15 9 24
38
25
23
110
2
1
4
1 1
12
9.
10..
11.
12
23
34
45
15
64
2 32
2 16
2 8
2 4
2 2
2 2
× × × =
× ×
/ \
/ \
/ \
/ \
/ \
22 2 2 2
81
3 27
3 9
3 3
3 3 3 3
3248
2 163
× × ×
× × ×
= ××
12.
13.
/ \
/ \
/ \
11623
24 2 2 2 3 36 2 2 3 3
2 2
=
= × × × = × × ×= ×
16 is GCF
LCM
14. ;
×× × × =
= = = =
2 3 3 72
23
27
1421
621
146
2 26
2 13
23
27
15.
16.
÷ ÷
÷ == × = =
× =
×
23
72
146
2 13
7 3 2117. . . .
because 1/10 1/10 = 1/100
see note for #17
( )× = ( )18.
19
2 4 1 2 2 88. . .
.. 1 3 2 1 2 73
1 32 11
. . .
.
.
× = ( ) see note for #17
or:
332 62 7 3
two decimal places in answer
.
/ \
/ \
/ \
/ \
/ \
22 2 2 2
81
3 27
3 9
3 3
3 3 3 3
3248
2 163
× × ×
× × ×
= ××
12.
13.116
23
24 2 2 2 3 36 2 2 3 3
2 2
=
= × × × = × × ×= ×
16 is GCF
LCM
14. ;
×× × × =
= = = =
2 3 3 72
23
27
1421
621
146
2 26
2 13
23
27
15.
16.
÷ ÷
÷ == × = =
× =
×
23
72
146
2 13
7 3 2117. . . .
because 1/10 1/10 = 1/100
see note for #17
( )× = ( )18.
19
2 4 1 2 2 88. . .
.. 1 3 2 1 2 73
1 32 11
. . .
.
.
× = ( ) see note for #17
or:
332 62 7 3
two decimal places in answer
.
( )200. . . .4 3 2 1 28× =
Systematic Review 2DLessonPractice 2D1. − + −( ) − − = − + ( ) −
= −4 7 3 2 16 4 2
1
2 2 2
66 16 2 2
4 10 3 5 6 8 2 4 7 30 4
28 30 4
+ − = −
−( ) − ( ) + = ( ) − += − + =
2. ÷
22
19 7 2 6 19 14 3619 14 36 31
23.
4.
− − ( ) −( ) + = − − −( ) += − + + =
− AA B A B A B A B
A A B B
−( ) + − = − +( ) + −= − +( ) + −( ) =
+ =
0
11 4 23
25. ÷ 1121 4 23
1214
23
36312
812
37112
30 1112
5 3 4
÷ + = +
= + = =
× +6. 22
2
7 8 4 5 3 16 7 2
15 16 7 2 22
5 5
− + −( ) = × + − + −( )= + − − =
− + −(
÷
7. )) = − ×( ) + −( ) −( ) = − + =
( ) = ( )
2
2
5 5 5 5 25 25 0
9 9 3 81 9 38. ÷ ÷ ÷ ÷ == =
× × =
=
+ =
9 3 3
25
78
47
15
524
2096
932
2796479
1 1
21
÷
9.
10.
66
3 4 6 3 4 6
12 6 3 2472 72
LCM is 96
y
11.
12.
×( ) × = × ×( )× = ×
=ees, see #11
13.
14.
10 8 6
10 28
10 8 6
2 64
− −( )−
−( ) −−
−
≠
≠≠
nno, see #13
15.
16.
127
74
4828
4928
4849
127
74
1
÷ ÷
÷
= =
=
aLGeBra 1
sYsteMatic reVieW 2D - sYsteMatic reVieW 2e
soLutions160
== =
× × =
=
+ =
9 3 3
25
78
47
15
524
2096
932
2796479
1 1
21
9.
10.
66
3 4 6 3 4 6
12 6 3 2472 72
LCM is 96
y
11.
12.
×( ) × = × ×( )× = ×
=ees, see #11
13.
14.
10 8 6
10 28
10 8 6
2 64
− −( )−
−( ) −−
−
≠
≠≠
nno, see #13
15.
16.
127
74
4828
4928
4849
127
74
1
÷ ÷
÷
= =
= 227
47
4849
38 33
06
180
50
× =
17. .
.
2.3000
448
2018
2018
5
5 2 52 5
0
5
18.
19.
. .
00
05 2 502 5
0
2
5 3 1 061 06
0
. .
.
. .
20.
== =
× × =
=
+ =
9 3 3
25
78
47
15
524
2096
932
2796479
1
9.
10.
66
3 4 6 3 4 6
12 6 3 2472 72
LCM is 96
y
11.
12.
×( ) × = × ×( )× = ×
=ees, see #11
13.
14.
10 8 6
10 28
10 8 6
2 64
− −( )−
−( ) −−
−
≠
≠≠
nno, see #13
15.
16.
127
74
4828
4928
4849
127
74
1
÷ ÷
÷
= =
= 227
47
4849
38 33
06
180
50
× =
17. .
.
2.3000
448
2018
2018
5
5 2 52 5
0
5
18.
19.
. .
00
05 2 502 5
0
2
5 3 1 061 06
0
. .
.
. .
20.
== =
× × =
=
+ =
9 3 3
25
78
47
15
524
2096
932
2796479
9.
10.
66
3 4 6 3 4 6
12 6 3 2472 72
LCM is 96
y
11.
12.
×( ) × = × ×( )× = ×
=ees, see #11
13.
14.
10 8 6
10 28
10 8 6
2 64
− −( )−
−( ) −−
−
≠
≠≠
nno, see #13
15.
16.
127
74
4828
4928
4849
127
74
1
÷ ÷
÷
= =
= 227
47
4849
38 33
06
180
50
× =
17. .
.
2.3000
448
2018
2018
5
5 2 52 5
0
5
18.
19.
. .
00
05 2 502 5
0
2
5 3 1 061 06
0
. .
.
. .
20.
== =
× × =
=
+ =
242096
932
2796479
9.
10.
66
3 4 6 3 4 6
12 6 3 2472 72
LCM is 96
y
11.
12.
×( ) × = × ×( )× = ×
=ees, see #11
13.
14.
10 8 6
10 28
10 8 6
2 64
− −( )−
−( ) −−
−
≠
≠≠
nno, see #13
15.
16.
127
74
4828
4928
4849
127
74
1
÷ ÷
÷
= =
= 227
47
4849
38 33
06
180
50
× =
17. .
.
2.3000
448
2018
2018
5
5 2 52 5
0
5
18.
19.
. .
00
05 2 502 5
0
2
5 3 1 061 06
0
. .
.
. .
20.
Systematic Review 2ELessonPractice 2E1.
2.
− + − + = − + − + =×
3 2 8 7 3 8 8 49 46
5
3 2
66 3 30 3 10
10 3 9 20 13 9 20
1
2 2
( ) = =
+( ) −
= −
=
÷ ÷
÷ ÷3.
669 9 20
160 20 8
2 3 2 3 3
−[ ]= =
+ + − = +( ) + −( ) =
÷
÷
4. A B A B A A B B A −−−( ) × = −( ) × = × =
+ + = +
2
42 6 2 11 7 2 11 5 11 55
8 45 9 3 8
B
5.
6.
÷
÷ 55 3 16
4 5 3 16 25 9 32
192 8 4 67
2 2 2
+ =
−( ) + ( ) − = + − =
( ) × −
7.
8. ÷ −− = × − −= − = −
× × = =
200 24 4 133
96 133 37
103
74
712
24572
5
69. 33 29
72
37
1113
37
1313
1113
77
3991
7791
1169
LessonPractice 2E1.
2.
− + − + = − + − + =×
3 2 8 7 3 8 8 49 46
5
3 2
66 3 30 3 10
10 3 9 20 13 9 20
1
2 2
( ) = =
+( ) −
= −
=
÷ ÷
÷ ÷3.
669 9 20
160 20 8
2 3 2 3 3
−[ ]= =
+ + − = +( ) + −( ) =
÷
÷
4. A B A B A A B B A −−−( ) × = −( ) × = × =
+ + = +
2
42 6 2 11 7 2 11 5 11 55
8 45 9 3 8
B
5.
6.
÷
÷ 55 3 16
4 5 3 16 25 9 32
192 8 4 67
2 2 2
+ =
−( ) + ( ) − = + − =
( ) × −
7.
8. ÷ −− = × − −= − = −
× × = =
200 24 4 133
96 133 37
103
74
712
24572
5
69. 33 29
72
37
1113
37
1313
1113
77
3991
7791
1169
10. + = × + ×
= + =11
1 2591
=
Cross multiplication always yields
a corrrect answer for addition
of fractions. In some cases, you
will have to reduce after finding
thhe answer.
6 is GCF
11.
12.
3054
5 69 6
59
10 10100
= ××
=
=== ×= × =
10 1010 10 100LCM
LCM may also be found using prime factors
y
( )+ + = + +
+ = +=
13.
14.
6 2 9 2 6 98 9 8 9
17 17
ees; see #13
Either
15. 378
114
378
228
3722
11522
÷ ÷= = =
method may be used
for dividing fractions
=
16.
17.
.
. .
45
3 1 1 395
1 24
155155
143
54
56
÷112
1512
5615
3 1115
004
4 001616
3
4
÷ = =
18.
19.
.
. .
.
groups of $.40
24
1 2
16
24
6 1 4412
.
$.
.
aLGeBra 1
sYsteMatic reVieW 2e - Lesson Practice 3a
soLutions 161
=
16.
17.
.
. .
45
3 1 1 395
1 24
155155
143
54
56
÷112
1512
5615
3 1115
004
4 001616
3
4
÷ = =
18.
19.
.
. .
.
groups of $.40
24
1 2
16
24
6 1 4412
.
$.
.
20. pper person
Lesson Practice 3ALessonPractice 3A1. − + + − = + −
− +( ) + −5 3 8 4 9 3 1
5 8 3
A A
A A 44 11
3 1 111 1
3 1
( ) =+ −( ) =
+ +=
A
A 22
4
5 4 3 8 4 4 9 3 120 3 32 4 9 3
A =
− ( ) + + ( ) − = + −− + + − = + −
Check:11
11 11=
2. 3 7 4 436 7 43
7 7
B B BB
− + + =+ =− −
Check:
66
366
6
3 6 6 7 4 6 43
18 6 7
B
B
=
=
( ) − ( ) + + ( ) =− + +224 43
43 43
4 6 7 3 174 3 17
3
==
− − + + + =− =+
3. Y Y YY
+
=
=
−
3
44
204
5
4 5
Check:
Y
Y
(( ) − + ( ) + + ( ) =− − + + + =
=
+ −
6 7 5 3 5 17
20 6 35 3 5 1717 17
5 34. Q Q 66 2 2 3 9
10 6 14
6 6
1010
20102
+ = +( ) +− =
+ +
=
=
Q
Q
Q
Q
CCheck: 5 2 3 2 6 2 2 2 3 9
10 6 6 4 5 914
( ) + ( ) − + ( ) = +( ) ++ − + = +
=
+
=
=
−
3
44
204
5
4 5
Check:
Y
Y
(( ) − + ( ) + + ( ) =− − + + + =
=
+ −
6 7 5 3 5 17
20 6 35 3 5 1717 17
5 34. Q Q 66 2 2 3 9
10 6 14
6 6
1010
20102
+ = +( ) +− =
+ +
=
=
Q
Q
Q
Q
CCheck: 5 2 3 2 6 2 2 2 3 9
10 6 6 4 5 914
( ) + ( ) − + ( ) = +( ) ++ − + = +
= 114
6 5 4 2 12 29 3 24
3 3
99
279
5. K K KK
K
− + − + = ⋅− =+ +
=
KK =
( ) − + ( ) − ( ) + = ⋅− + − + =
3
5 4 3 3 2 12 2
18 5 12 3 2 24
Check: 6 3
224 24=
6. 5 2 8 7 3 4 12 1 13
1 1
22
142
C C CC
C
C
− − + − = ⋅ +− =
+ +
=
==
( ) − ( ) − + − ( ) = ⋅ +− − + − =
7
2 7 8 7 7 3 4 135 14 8 7 7 12
Check: 5 7++
=
+ = +− = −
=
=
113 13
4 6 2 124 2 12 6
22
62
3
7. A AA A
A
A
Check: 4 33( ) + = ( ) ++ = +
=
− + = +−
6 2 3 12
12 6 6 1218 18
10 2 3 5 218
8. B B BB 55 21 3
33
183
6
2 6 3 5 6 21
60
BB
B
= −
=
=
( ) − ( ) + = ( ) +Check: 10 6
−− + = +=
− + = − +− = +
12 3 30 2151 51
6 8 3 7 2 129 5 12 8
4
9. C C C CC C
C44
204
5
6 5 8 3 5 7 5 2 5 12
30 8 15
=
=
( ) − + ( ) = ( ) − ( ) +− +
C
Check:
== − +=
− = − −+ = − +
= −
35 10 1237 37
6 10 2 346 2 34 10
88
aLGeBra 1
Lesson Practice 3a - Lesson Practice 3B
soLutions162
++ = +
=
− + = +−
6 2 3 12
12 6 6 1218 18
10 2 3 5 218
B B BB 55 21 3
33
183
6
2 6 3 5 6 21
60
BB
B
= −
=
=
( ) − ( ) + = ( ) +Check: 10 6
−− + = +=
− + = − +− = +
12 3 30 2151 51
6 8 3 7 2 129 5 12 8
4
9. C C C CC C
C44
204
5
6 5 8 3 5 7 5 2 5 12
30 8 15
=
=
( ) − + ( ) = ( ) − ( ) +− +
C
Check:
== − +=
− = − −+ = − +
= −
35 10 1237 37
6 10 2 346 2 34 10
88
10. D DD D
D 22483
6 3 10 2 3 34
18 10 6 3428
D = −
−( ) − = − −( ) −− − = −
−
Check:
== −28
11. − − − + + =+ =− −
=
3 3 6 10 5 102 10
2 2
8
A A AA
A
Check: − ( ) − − ( ) + ( ) + =− − − + + =
=
3 8 3 6 8 10 8 5 10
24 3 48 80 5 1010 10
122. − − + + − = ⋅− =+ +
=
5 4 10 7 7 114 3 77
3 3
44
80
B B BB
B44
20
5 20 20 4 10 20 7 7 11
100 20
B =
− ( ) − ( ) + + ( ) − = ⋅− −
Check:
++ + − ==
− + − + = −= − +
4 200 7 7777 77
4 7 3 5 10 78 100 7 3
213. R R RR
888
968
12
4 12 7 12 3 5 12 10 74
2
R
R
=
=
− ( ) + ( ) − + ( ) = −−
Check:88 84 3 60 100 7
93 93
7 8 6 5 3 5 7
2 2 8
+ − + = −=
− + − + = ⋅ −− + =
14. Q Q
Q
− −
−−
=−
= −
− −( ) + − +
2 2
22
623
7 3 8 6 5
Q
Q
Check: −−( ) = ⋅ −+ − − = −
=
3 3 5 7
21 8 6 15 15 78 8
R R RR
888
968
12
4 12 7 12 3 5 12 10 74
2
R
R
=
=
− ( ) + ( ) − + ( ) = −−
Check:88 84 3 60 100 7
93 93
7 8 6 5 3 5 7
2 2 8
+ − + = −=
− + − + = ⋅ −− + =
14. Q Q
Q
− −
−−
=−
= −
− −( ) + − +
2 2
22
623
7 3 8 6 5
Q
Q
Check: −−( ) = ⋅ −+ − − = −
=
3 3 5 7
21 8 6 15 15 78 8
Lesson Practice 3B1. − − + − + =
− =+ +
=
=
3 5 4 6 2 193 11 19
11 11
33
303
A A AA
A
A 110
3 10 5 4 10 6 2 10 19
30 5 40 6 2
Check: − ( ) − + ( ) − + ( ) =− − + − + 00 19
19 19
8 6 5 3 3 4110 9 41
9
==
− + − − =− =+ +
2. B B BB
99
1010
50105
8 5 6 5 5 3 3 5 41
40 6
B
B
=
=
( ) − + ( ) − − ( ) =−
Check:
++ − − ==
− + − + + =− + =
25 3 15 4141 41
5 3 6 2 4 139 7 13
3. Y Y YY
− −
−−
=−
= −
− − + − −
7 7
99
6923
5 23
3 6 2
Y
Y
Check:33
2 23
4 13
103
3 123
43
4 13
183
7
+ −
+ =
+ + − + =
+ = 113
6 7 1313 13
8 7 4 3 7 4 10
4 3 47
+ ==
− + − − = + ×+ =
−
4. Q Q Q
Q
33 3
44
444
11
8 11 11 7 4 3 11 7 4
−
=
=
( ) ( ) ( )
Q
Q
Check:
aLGeBra 1
Lesson Practice 3B - Lesson Practice 3B
soLutions 163
++ − − ==
− + − + + =− + =
25 3 15 4141 41
5 3 6 2 4 139 7 13
3. Y Y YY
− −
−−
=−
= −
− − + − −
7 7
99
6923
5 23
3 6 2
Y
Y
Check:33
2 23
4 13
103
3 123
43
4 13
183
7
+ −
+ =
+ + − + =
+ = 113
6 7 1313 13
8 7 4 3 7 4 10
4 3 47
+ ==
− + − − = + ×+ =
−
4. Q Q Q
Q
33 3
44
444
11
8 11 11 7 4 3 11 7 4
−
=
=
( ) − ( ) + − − ( ) = +
Q
Q
Check: ××− + − − =
=
1088 11 7 4 33 47
47 47
5. 8 4 6 3 5 8 19 9 63
9 9
99
729
2M M MM
M
M
− − − + = −− =+ +
=
==
( ) − ( ) − − + ( ) = −− − − + =
8
8 8 4 8 6 3 5 8 8 1
64 32 6 3 40 6
2Check:
3363 63
7 4 5 8 5 44 3 29
3 3
4
2
=
− + − + = +− =+ +
6. C C CC
C44
324
8
7 8 4 8 5 8 8 5 4
56 32 5 8
2
=
=
( ) − ( ) + − + ( ) = +
− + −
C
Check:
++ = +=
− − = + +− = +
=
8 5 429 29
11 4 18 2 107 3 10 18
44
2
7. A A A AA A
A 2284
7
11 7 4 7 18 2 7 7 1077 28 18
A =( ) − ( ) − = ( ) + ( ) +
− −Check:
== + +=
− − + = − − −− − =
14 7 1031 31
2 10 15 5 8 40 4 68 10 4
8. B B B BB B −−
− − = − +−−
= −−
=
( ) −
468 4 46 10
1212
3612
3
2 3 10
B BB
B
Check: 33 15 5 8 3 40 4 3 6
6 30 15 5 24 40 12 634
( ) − + = ( ) − − ( ) −− − + = − − −
− == −
++ = +=
− − = + +− = +
=
8 5 429 29
11 4 18 2 107 3 10 18
44
A A A AA A
A 2284
7
11 7 4 7 18 2 7 7 1077 28 18
A =( ) − ( ) − = ( ) + ( ) +
− −Check:
== + +=
− − + = − − −− − =
14 7 1031 31
2 10 15 5 8 40 4 68 10 4
8. B B B BB B −−
− − = − +−−
= −−
=
( ) −
468 4 46 10
1212
3612
3
2 3 10
B BB
B
Check: 33 15 5 8 3 40 4 3 6
6 30 15 5 24 40 12 634
( ) − + = ( ) − − ( ) −− − + = − − −
− == −34
9. 3 6 2 10 2 65 6 8 6
5 8 6 633
123
C C C CC C
C CC
C
− + = − +− = +
− = +−−
=−
== −
−( ) − + −( ) = −( ) − −( ) +− − − = −
4
3 4 6 2 4 10 4 2 4 612 6 8
Check:440 8 6
26 26
2 8 5 3 2 63 8 5 6
3
+ +− = −
− − = − − +− − = − +
−
10. D D D DD D
D ++ = +
=
=( ) − − ( ) = − ( ) − ( )
5 6 822
142
7
2 7 8 5 7 3 7 2 7
DD
D
Check: ++− − = − − +
− = −
− + − + = ×
614 8 35 21 14 6
29 29
8 6 3 2 3 4 339
11. K K KKK
K
K
− =+ +
=
=
( ) − + ( ) −
3 132
3 3
99
1359
15
8 15 6 3 15 2 15Check: (( ) + = ×− + − + =
=
+ + + =
3 4 33
120 6 45 30 3 132132 132
6 612. B B B B ++ − ++ = +
− = −= −
−( ) + −( )
5 2 93 6 4 146 14 4 3
8
8 8
BB B
B BB
Check:
++ −( ) + = −( ) + − −( ) +− + = − + + +
− = −
8 6 6 8 5 2 8 9
24 6 48 5 16 918 18
113. − + = − + −− + = −− − = − −
−
2 12 2 6 6 122 12 8 182 8 18 12
C C CC CC C
11010
3010
3
2 3 12 2 3 6 6 3 12
C
C−
= −−
=
− ( ) + = ( ) − + ( ) −Check:
−− + = − + −=
6 12 6 6 18 126 6
aLGeBra 1
Lesson Practice 3B - sYsteMatic reVieW 3c
soLutions164
++ − ++ = +
− = −= −
−( ) + −( )
5 2 93 6 4 146 14 4 3
8
8 8
BB B
B BB
Check:
++ −( ) + = −( ) + − −( ) +− + = − + + +
− = −
8 6 6 8 5 2 8 9
24 6 48 5 16 918 18
113. − + = − + −− + = −− − = − −
−
2 12 2 6 6 122 12 8 182 8 18 12
C C CC CC C
11010
3010
3
2 3 12 2 3 6 6 3 12
C
C−
= −−
=
− ( ) + = ( ) − + ( ) −Check:
−− + = − + −=
6 12 6 6 18 126 6
14. 10 3 9 3 51 3 16 6 18
6 6
66
246
4
X X XX
X
X
− − + − = +− =+ +
=
=
÷
Checck: 10 4 3 4 9 3 4 51 3 140 12 9 3 4 17 1
18
( ) − ( ) − + − ( ) = +− − + − = +
÷
== 18
Systematic Review 3CSystematicReview 3C1.
2.
XX
X
X
+ =+ − = −
=
+ =
3 93 3 9 3
6
6 10XX
X
XX
XX
Q
+ − = −=
+ =+ − = −
==
−
6 6 10 64
2 5 112 5 5 11 5
2 63
4 2
3
4.
.
==− + = +
==
+ = ++ − = + −
10
4 2 2 10 2
4 12
3
4 2 2 84 2 2 2 8 2
Q
Q
Q
X XX X
5.
44 2 64 2 2 2 6
2 63
3 5 2 73 5 5 2
X XX X X X
XX
Y YY
= +− = − +
==
+ = ++ − =
6.YY
Y YY Y Y Y
Y
Q Q
Q Q Q
+ −= +
− = − +=
+ = −+ − =
7 53 2 2
3 2 2 2 22
4 3 6
4 3
7.
−− −= −
+ = − +==
Q
Q
Q
Q
Q
6
4 2 6
4 6 2 6 6
10 2
5
==− + = +
==
+ = ++ − = + −
10
4 2 2 10 2
4 12
3
4 2 2 84 2 2 2 8 2
Q
Q
Q
X XX X
5.
44 2 64 2 2 2 6
2 63
3 5 2 73 5 5 2
X XX X X X
XX
Y YY
= +− = − +
==
+ = ++ − =
6.YY
Y YY Y Y Y
Y
Q Q
Q Q Q
+ −= +
− = − +=
+ = −+ − =
7 53 2 2
3 2 2 2 22
4 3 6
4 3
7.
−− −= −
+ = − +==
Q
Q
Q
Q
Q
6
4 2 6
4 6 2 6 6
10 2
5
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
2R 8 3R 22R 2R 8 3R 2R 2
8 R 28 2 R 2 2
R 10
9 3 4 11
6 76 7
1 2 3 2 3
4 6
4 6
3 4 6 3 5
3 4 36 3 25
12 108 25 120 25 95
14 9 2 3÷ 6 2
14 9 4 3÷ 6 4
9 36
4
9 126
9 2 7
43
610
÷ 23
43
610
32
65
1 15
.1 7 .8 5 8 6
.1 3 6
Three decimal places in answer
8 7 56
4 4 4 16
2 2; 3 3; 4 2 2; so LCM 2 2 3 12
12 12
12 23
12 14
X
It is not necessary to write in "1" when
dividing terms, unless you wish.
6 8 3X; X 4 23
2 2; 5 5; 4 2 2; so LCM 2 2 5 20
4 20 35
X 20 34
20 32
12X 15 30; X 1 14
2 2
2 2
2
1
2
5 1
2
6 4 3
5 10
1
( ) ( )
( )
( ) ( )( )
( )
( ) ( )
( )
( ) ( ) ( )
( )( ) ( )( )
( ) ( ) ( )
+ = −− + = − −
= −+ = − +
=
− < −< −<
− − < ×− <
<
− × + × − + =− × + × − + =
− + − + = − + = −
− + − × =− + − × =
− ×
=
− = − =
× = × × = =
×
− − =
− = − − == = = × = × × =
+ =
+ = =
= = = × = × × =
+ =
+ = =
aLGeBra 1
sYsteMatic reVieW 3c - sYsteMatic reVieW 3D
soLutions 165
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
2R 8 3R 22R 2R 8 3R 2R 2
8 R 28 2 R 2 2
R 10
9 3 4 11
6 76 7
1 2 3 2 3
4 6
4 6
3 4 6 3 5
3 4 36 3 25
12 108 25 120 25 95
14 9 2 3÷ 6 2
14 9 4 3÷ 6 4
9 36
4
9 126
9 2 7
43
610
÷ 23
43
610
32
65
1 15
.1 7 .8 5 8 6
.1 3 6
Three decimal places in answer
8 7 56
4 4 4 16
2 2; 3 3; 4 2 2; so LCM 2 2 3 12
12 12
12 23
12 14
X
It is not necessary to write in "1" when
dividing terms, unless you wish.
6 8 3X; X 4 23
2 2; 5 5; 4 2 2; so LCM 2 2 5 20
4 20 35
X 20 34
20 32
12X 15 30; X 1 14
2 2
2 2
2
1
2
5 1
2
6 4 3
5 10
( )
( ) ( )( )
( )
( ) ( )
( )
( ) ( ) ( )
( )( ) ( )( )
( ) ( ) ( )
+ = −− + = − −
= −+ = − +
=
− < −< −<
− − < ×− <
<
− × + × − + =− × + × − + =
− + − + = − + = −
− + − × =− + − × =
− ×
=
− = − =
× = × × = =
×
− − =
− = − − == = = × = × × =
+ =
+ = =
= = = × = × × =
+ =
+ = =
19. 3 3 5 5 9 3 3 3 3 5 45
45 19
45 15
= = = × = × × =
( ) +
; ; ; so LCM
X 55 23
45 15
5 30 9 5 21 4 15
5 5 4
9( ) = ( )
+ = = − = −
= =
X X X; ;
;
20. 22 2 8 2 2 2
2 2 2 5 40
40 38
40 15
5 8
× = × ×= × × × =
( ) − ( ) =
;
so LCM
X 110 40 34
15 8 30 8 15 178
( )
− = − = = −X X X; ;
Systematic Review 3DSystematicReview 3D1.
2.
YY
Y
B
− =− + = +
=
−
3 103 3 10 3
13
2 55 132 18
2 2 18 29
3 6 93 15
3 3 15 3
====
+ = −= −= −
BB ÷
B
CC
C
÷
÷ ÷
3.
CC
DD
DD
EEE
= −
− ====
− = −==
5
2 5 12 6
2 2 6 23
4 3 34 0
0
3
4.
5.
6.
÷ ÷
XX XX X X X
XX
X
+ = − −+ = − + −
= −= −= −
8 2 23 2 2 2 10
5 105 5 10 5
2÷ ÷
7. 22 2 3 62 3 6 2
41 1 4
4
Y YY Y
YYY
− = −− = − +− = −
−( ) −( ) = −( ) −( )=
CC
DD
DD
EEE
= −
− ====
− = −==
5
2 5 12 6
2 2 6 23
4 3 34 0
0
3
4.
5.
6.
÷ ÷
XX XX X X X
XX
X
+ = − −+ = − + −
= −= −= −
8 2 23 2 2 2 10
5 105 5 10 5
2÷ ÷
7. 22 2 3 62 3 6 2
41 1 4
4
Y YY Y
YYY
− = −− = − +− = −
−( ) −( ) = −( ) −( )=
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
Z 8 2Z 18Z 2Z 18 8
Z 10
1 Z 1 10
Z 10
3 2 2 24 ÷ 3
12 812 8
17 3 20 7 0 1
6 8
6 8
6 2 5 10 ÷5
4 25 10 ÷25
100 10 ÷25
90 ÷25 3 35
or 3.6
7 6 4 5 3
13 6 169 36 133
56
37
÷ 23
56
37
32
1528
14.
12. 168. 12
48 48
2 2; 5 5; 10 2 5; LCM 2 5 10
10 65
X 10 710
10 52
X
12X 7 25X7 13X
7 ÷13 13X ÷13713
X
100 10 10; 1000 10 10 10
LCM 10 10 10 1000
1000 .83 1000 .04X 1000 .325
830 40X 32540X 505
X 50540
12 58
or 12.625
10 10; 100 10 10;
LCM 10 10 100
100 .18 100 .2X 100 .17
18 20X 1720X 1
X 120
or .05
10 10; 100 10 10;
LCM 10 10 100
100 .8X 100 1.3 100 7 100 .24
80X 130 700 2480X 594
X 59480
7 1740
or 7.425
10 10; 100 10 10;
LCM 10 10 100
100 8.2 100 4 100 .08X
820 400 8X420 8X
X 4208
52 12
or 52.5
2 2
2 2
2 2
2
2 1 5
[ ]
( ) ( )
[ ][ ]
( )
( )
( )
( ) ( )( )
( )
( ) ( ) ( )
( )
( ) ( )
( ) ( )
( )( ) ( )
( )
+ = +− = −− =
− − = −= −
× × − > −− > −
> −
− − < + +− <
<
− × − =
× − =− =
=
− − − + − =
− − = − =
× = × × =
= = = × = × =
+ =
+ ===
=
= × = × ×= × × =
+ =+ =
= −
= −
= − −
= = ×= × =
+ =+ =
= −
= − −
= = ×= × =
+ = ++ = +
=
= =
= = ×= × =
− =− =
=
= =
aLGeBra 1
sYsteMatic reVieW 3D - sYsteMatic reVieW 3e
soLutions166
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
Z 8 2Z 18Z 2Z 18 8
Z 10
1 Z 1 10
Z 10
3 2 2 24 ÷ 3
12 812 8
17 3 20 7 0 1
6 8
6 8
6 2 5 10 ÷5
4 25 10 ÷25
100 10 ÷25
90 ÷25 3 35
or 3.6
7 6 4 5 3
13 6 169 36 133
56
37
÷ 23
56
37
32
1528
14.
12. 168. 12
48 48
2 2; 5 5; 10 2 5; LCM 2 5 10
10 65
X 10 710
10 52
X
12X 7 25X7 13X
7 ÷13 13X ÷13713
X
100 10 10; 1000 10 10 10
LCM 10 10 10 1000
1000 .83 1000 .04X 1000 .325
830 40X 32540X 505
X 50540
12 58
or 12.625
10 10; 100 10 10;
LCM 10 10 100
100 .18 100 .2X 100 .17
18 20X 1720X 1
X 120
or .05
10 10; 100 10 10;
LCM 10 10 100
100 .8X 100 1.3 100 7 100 .24
80X 130 700 2480X 594
X 59480
7 1740
or 7.425
10 10; 100 10 10;
LCM 10 10 100
100 8.2 100 4 100 .08X
820 400 8X420 8X
X 4208
52 12
or 52.5
2 2
2 2
2 2
2
2 1 5( ) ( )
( )
( )
( )
( ) ( )( )
( )
( ) ( ) ( )
( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( )
+ = +− = −− =
− − = −= −
× × − > −− > −
> −
− − < + +− <
<
− × − =
× − =− =
=
− − − + − =
− − = − =
× = × × =
= = = × = × =
+ =
+ ===
=
= × = × ×= × × =
+ =+ =
= −
= −
= − −
= = ×= × =
+ =+ =
= −
= − −
= = ×= × =
+ = ++ = +
=
= =
= = ×= × =
− =− =
=
= =
Systematic Review 3E1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
2X 7 3X 4 10 1X 3 9
X 6
3Y 8 2 2Y 9 4 5Y 6 10
Y 4
2X 2 7 X X 6 6 12X 5 11
2X 6X 3
2B 3 5B 1 2 3 2 9
3B 4 2 5 9
3B 19 43B 15B 5
3Q 2 Q 3 2 2 2
4Q 2 3 4 2
4Q 12 2 2
4Q 12
Q 3
5X 5 X 3 3X X 4 2
4X 2 2X 84X 2X 8 2
2X 6X 3
2Y 4 Y 9 2Y 4 4Y 113Y 5 2Y 7
3Y 2Y 7 5Y 2
4Q 2 5Q 2 3Q 6
Q 4 3Q 6
4 6 3Q Q
10 2Q
5 Q
7 3 3 7 4 4 16 4 64
8 5 4 2 11 8 9 2 121
8 81 2 1218 162 121 291
4 8 6 3 3 6 7 3 4
4 8 6 9 3 6 49 3 4
32 6 9 3 6 147 4
35 146 111
15 6 8 3÷3 10 9 40 ÷8
15 6 64 3÷3 10 81 40 ÷8
15 6 64 1 10 81 5
74 86 12
34
83
÷ 21
34
83
12
1
1.7.8
5 86
1.36
two decimal places in answer
19 6 114
6 6 6 6 36
6 6 6
7 3 7 3 4
3 3 1; 6 2 3; 8 2 2 2
LCM 2 2 2 3 24
24 78
24 23
X 24 16
21 16X 416X 17
X 1 116
10 10; 100 10 10;
LCM 10 10 100
100 .03X 100 .6 100 .75
3X 60 753X 135X 45
( )( )
( )
( )
( ) ( )( ) ( )
( )
( ) ( )( ) ( )
( ) ( )( ) ( )
( )( )
( ) ( ) ( )
( )( )
( )
( )
− + + − = −+ =
=
+ − − = − ++ =
=
− + + − = + −+ =
==
− + + + = + ++ = +
= −==
− + = + −− = −
= − +==
+ − − = − ++ = +
− = −==
− + + = − − + ++ = +
− = −=
− + + + = −+ = −+ = −
==
− × − = × − = × =
+ + × + = + × += + × += + + =
× − + + − − × + =× − + + − − × + =
− + + − − + =+ − = −
− + + − + − =− + + − + − =
− + + − + − =− = −
× = × × =
− = −
− = − = − = −
− − − = − + = −− − − = − + = −= × = × = × ×
= × × × =
+ =
+ == −
= −
= = ×= × =
− =− =
==
SystematicReview 3E
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
2X 7 3X 4 10 1X 3 9
X 6
3Y 8 2 2Y 9 4 5Y 6 10
Y 4
2X 2 7 X X 6 6 12X 5 11
2X 6X 3
2B 3 5B 1 2 3 2 9
3B 4 2 5 9
3B 19 43B 15B 5
3Q 2 Q 3 2 2 2
4Q 2 3 4 2
4Q 12 2 2
4Q 12
Q 3
5X 5 X 3 3X X 4 2
4X 2 2X 84X 2X 8 2
2X 6X 3
2Y 4 Y 9 2Y 4 4Y 113Y 5 2Y 7
3Y 2Y 7 5Y 2
4Q 2 5Q 2 3Q 6
Q 4 3Q 6
4 6 3Q Q
10 2Q
5 Q
7 3 3 7 4 4 16 4 64
8 5 4 2 11 8 9 2 121
8 81 2 1218 162 121 291
4 8 6 3 3 6 7 3 4
4 8 6 9 3 6 49 3 4
32 6 9 3 6 147 4
35 146 111
15 6 8 3÷3 10 9 40 ÷8
15 6 64 3÷3 10 81 40 ÷8
15 6 64 1 10 81 5
74 86 12
34
83
÷ 21
34
83
12
1
1.7.8
5 86
1.36
two decimal places in answer
19 6 114
6 6 6 6 36
6 6 6
7 3 7 3 4
3 3 1; 6 2 3; 8 2 2 2
LCM 2 2 2 3 24
24 78
24 23
X 24 16
21 16X 416X 17
X 1 116
10 10; 100 10 10;
LCM 10 10 100
100 .03X 100 .6 100 .75
3X 60 753X 135X 45
2 2
2 2 2
2 2
2 2
4
2 2
3 8 4
( ) ( )
( ) ( )
( )
( )
[ ]
( )( )
( )
( )
( ) ( )( ) ( )
( )
( ) ( )( ) ( )
( ) ( )( ) ( )
( )( )
( ) ( ) ( )
( )( )
( )
( )
− + + − = −+ =
=
+ − − = − ++ =
=
− + + − = + −+ =
==
− + + + = + ++ = +
= −==
− + = + −− = −
= − +==
+ − − = − ++ = +
− = −==
− + + = − − + ++ = +
− = −=
− + + + = −+ = −+ = −
==
− × − = × − = × =
+ + × + = + × += + × += + + =
× − + + − − × + =× − + + − − × + =
− + + − − + =+ − = −
− + + − + − =− + + − + − =
− + + − + − =− = −
× = × × =
− = −
− = − = − = −
− − − = − + = −− − − = − + = −= × = × = × ×
= × × × =
+ =
+ == −
= −
= = ×= × =
− =− =
==
aLGeBra 1
sYsteMatic reVieW 3e - Lesson Practice 4B
soLutions 167
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
2X 7 3X 4 10 1X 3 9
X 6
3Y 8 2 2Y 9 4 5Y 6 10
Y 4
2X 2 7 X X 6 6 12X 5 11
2X 6X 3
2B 3 5B 1 2 3 2 9
3B 4 2 5 9
3B 19 43B 15B 5
3Q 2 Q 3 2 2 2
4Q 2 3 4 2
4Q 12 2 2
4Q 12
Q 3
5X 5 X 3 3X X 4 2
4X 2 2X 84X 2X 8 2
2X 6X 3
2Y 4 Y 9 2Y 4 4Y 113Y 5 2Y 7
3Y 2Y 7 5Y 2
4Q 2 5Q 2 3Q 6
Q 4 3Q 6
4 6 3Q Q
10 2Q
5 Q
7 3 3 7 4 4 16 4 64
8 5 4 2 11 8 9 2 121
8 81 2 1218 162 121 291
4 8 6 3 3 6 7 3 4
4 8 6 9 3 6 49 3 4
32 6 9 3 6 147 4
35 146 111
15 6 8 3÷3 10 9 40 ÷8
15 6 64 3÷3 10 81 40 ÷8
15 6 64 1 10 81 5
74 86 12
34
83
÷ 21
34
83
12
1
1.7.8
5 86
1.36
two decimal places in answer
19 6 114
6 6 6 6 36
6 6 6
7 3 7 3 4
3 3 1; 6 2 3; 8 2 2 2
LCM 2 2 2 3 24
24 78
24 23
X 24 16
21 16X 416X 17
X 1 116
10 10; 100 10 10;
LCM 10 10 100
100 .03X 100 .6 100 .75
3X 60 753X 135X 45
2 2
2 2 2
2 2
2 2
4
2 2
3 8 4
( ) ( )
( ) ( )
( )
( ) ( ) ( )
( )
[ ]
( )( )
( )
( )
( ) ( )( ) ( )
( )
( ) ( )( ) ( )
( ) ( )( ) ( )
( )( )
( ) ( ) ( )
− + + − = −+ =
=
+ − − = − ++ =
=
− + + − = + −+ =
==
− + + + = + ++ = +
= −==
− + = + −− = −
= − +==
+ − − = − ++ = +
− = −==
− + + = − − + ++ = +
− = −=
− + + + = −+ = −+ = −
==
− × − = × − = × =
+ + × + = + × += + × += + + =
× − + + − − × + =× − + + − − × + =
− + + − − + =+ − = −
− + + − + − =− + + − + − =
− + + − + − =− = −
× = × × =
− = −
− = − = − = −
− − − = − + = −− − − = − + = −= × = × = × ×
= × × × =
+ =
+ == −
= −
= = ×= × =
− =− =
==
Lesson Practice 4ALessonPractice 4A1.
2.
5 4 3 5 4 5 3
6 2 3 1
+( ) = ( ) + ( )+ +( ) = 66 2 6 3 6 1
7 7 7
3 4 3 3 4 3
( ) + ( ) + ( )+( ) = ++( ) = ( ) +
3.
4.
A B A B
C B C 33
5 2 3 3 4 5 2 5 3 5 3 5 4
8
B
X Y X X Y X
A
( )+ − +( ) = ( ) + ( ) − ( ) + ( )5.
6. ++ + +( ) = ( ) + ( ) + ( ) + ( )+ = +( )
3 8 4 8 8 3 8 8 8 4
6 6 6
B A A B A
X Y X Y7.
88.
9.
10.
8 16 8 2
14 21 7 2 3
2 6 2
A B A B
X Y X Y
M N
+ = +( )+ = +( )
− − = − MM N
B C B C
X A X A
+( )+ = +( )+ = +( )
3
6 18 6 3
15 10 5 3 2
5
11.
12.
13. XX
X divide
XX
+ =+( ) = ( )+ =
=
15 45
5 3 5 9
3 96
out the 5s:
144. 10 16 26
2 5 8 2 13
5
X
X divide
X
+ =+( ) = ( )+
out the 2s:
88 135 5
1
13 26 39 52
13 2 3 13 4
===
− + =− +( ) = ( )
XX
Y Y
Y Y di
15.
vvide
YY
Y
A A
out the 13s:
4 2 44 6
64
1 12
8 10 6
− ==
= =
− −
MM N
B C B C
X A X A
+ = +( )+ = +( )
3
6 18 6 3
15 10 5 3 2
5
11.
12.
13. XX
X divide
XX
+ =+( ) = ( )+ =
=
15 45
5 3 5 9
3 96
out the 5s:
144. 10 16 26
2 5 8 2 13
5
X
X divide
X
+ =+( ) = ( )+
out the 2s:
88 135 5
1
13 26 39 52
13 2 3 13 4
===
− + =− +( ) = ( )
XX
Y Y
Y Y di
15.
vvide
YY
Y
A A
out the 13s:
4 2 44 6
64
1 12
8 10 6
− ==
= =
− −16. ==− −( ) = ( )
− ==
14
2 4 5 3 2 7
5 712
A A divide
AA
out the 2s:
117. 12 21 30
3 4 7 3 10
4
X
X divide
X
+ =+( ) = ( ) out the 3s:
++ ==
=
− =−( ) = ( )
7 104 3
34
8 28 12
4 2 7 4 3
X
X
X
X divide
18.
outt the 4s:
2 7 32 10
5
XXX
− ===
Lesson Practice 4BLessonPractice 4B1.
2.
8 5 2 8 5 8 2
5 4 3 2
+( ) = ( ) + ( )− +( ) = 55 4 5 3 5 2
9 9 9
5 2 4 5 2
( ) − ( ) + ( )+( ) = ( ) + ( )+( ) =
3.
4.
C D C D
C D C(( ) + ( )+ +( ) = ( ) + ( ) + ( )
− + +
5 4
3 4 3 3 3 4
2 3 2
D
X Y X X Y X
X Y Y
5.
6. (( ) = −( )( ) + −( )( ) + −( )( )+ = +( )
2 3 2 2 2
8 12 4 2 3
X Y Y
X Y X Y7.
8..
9.
− − = − −( ) − +( )+ = +(
7 21 7 3 7 3
18 24 6 3 4
X Y X Y or X Y
A B A B))+ =+( ) = ( )+ =+( ) = ( )
10.
11.
8 10 16
2 4 5 2 8
6 3 15
3 2 1 3 5
X
X
A
A
112.
13.
8 10 20
2 4 5 2 10
8 32 40
8 4 8 5
A
A
X
X
+ =+( ) = ( )
+ =+( ) = ( )
XXX
Y
Y
YY Y
+ ==
+ =+( ) = ( )+ =
= =
4 51
18 27 45
9 2 3 9 5
2 3 52 2
14.
; 11
15 10 5 25
5 3 2 5 5
4 2 54 7
74
1
aLGeBra 1
Lesson Practice 4B - Lesson Practice 4B
soLutions168
+ =+( ) = ( )+ =+( ) = ( )
10.
11.
8 10 16
2 4 5 2 8
6 3 15
3 2 1 3 5
X
X
A
A
112.
13.
8 10 20
2 4 5 2 10
8 32 40
8 4 8 5
A
A
X
X
+ =+( ) = ( )
+ =+( ) = ( )
XXX
Y
Y
YY Y
+ ==
+ =+( ) = ( )+ =
= =
4 51
18 27 45
9 2 3 9 5
2 3 52 2
14.
; 11
15 10 5 25
5 3 2 5 5
4 2 54 7
74
1
15. X X
X X
XX
X
− + =− +( ) = ( )
− ==
= = 334
9 6 12 18
3 3 2 4 3 6
2 688
16.
1
C C
C C
CCC
− − =− −( ) = ( )
− − =− =
= −
77.
18
14 42 56 28
14 3 4 14 2
5 3 25 5
1
M M
M M
MMM
− + =− +( ) = ( )
− ===
.. 6 16 4 20
2 3 8 2 2 10
8 1018
A A
A A
AA
− − =− −( ) = ( )
− ==
Systematic Review 4CSystematicReview 4C1.
2.
4 3 4 4 12
5 6
A B A B
X Y
+ +( ) = + +− + ++( ) = − + +− + +( ) = − + +
Z X Y Z
Q T Q T
5 5 30 5
3 2 4 3 7 6 12 9 21
2 2
3.
4. XX Y X Y
Y X Y X
+ −( ) = + −+ = +( ) = ( )
3 5 4 6 10
15 30 10 5 3 6 5 25.
6.
;
112 6 15 3 4 2 3 5
24 18 30 6 4 3
Q Y Q Y
Q Y Q Y
+ = +( ) = ( )+ = +( )
;
;7. == ( )− = −( ) = ( )
− < +− <
6 5
36 14 10 2 18 7 2 5
3 9 4 1
6
2
8.
9.
A B A B;
44 1
6 5
6 5
4 16 24
4 4 4 6
4 610
3
+− <− <
− =−( ) = ( )− =
=
10.
11.
X
X
XX
00 42 18
6 5 7 6 3
5 7 37 3 57 2
27
− =−( ) = ( )− =− = −− = −
= −−
=
Y
Y
YYY
Y 227
24 56 16
8 3 7 8 2
4 2
2
36 72
;
112 6 15 3 4 2 3 5
24 18 30 6 4 3
Q Y Q Y
Q Y Q Y+ = +( );
;7. == ( )− = −( ) = ( )
− < +− <
6 5
36 14 10 2 18 7 2 5
3 9 4 1
6
2
8.
9.
A B A B;
44 1
6 5
6 5
4 16 24
4 4 4 6
4 610
3
+− <− <
− =−( ) = ( )− =
=
10.
11.
X
X
XX
00 42 18
6 5 7 6 3
5 7 37 3 57 2
27
− =−( ) = ( )− =− = −− = −
= −−
=
Y
Y
YYY
Y 227
24 56 16
8 3 7 8 2
4 2
2
36 72
12.
13.
− + =− +( ) = ( )
==
− = +
Q
Q
Q
Q
A 445
9 4 9 8 5
4 8 59 898
1 18
10 10
−( ) = +( )− = +− =− = = −
= ×
A
AA
A
14. 11 100 10 10
10 10 100
100 2 100 03
; ;
LCM
. .
= ×= × =( ) − (15. X )) = ( )
− ===
= × = ×
100 97
20 3 9720 100
5
3 3 1 4 2 2 6
.
; ;
XXX
16. == ×= × × =
( ) + ( ) = ( )
2 3
2 2 3 12
12 34
12 13
12 56
9
3 4 2
;
LCM
17. Q
++ ==
=
= × = ×= ×
4 10
4 1
14
10 10 1 100 10 10
10 10
Q
Q
Q
18. ; ;
LCM ==
−( ) + ( ) = ( )− + =
100
100 7 100 8 100 12
70 80 121
19. . . .A A
A A00 12
1210
1 15
1 2
18 9
4 75 64
A
A
or
=
=
= .
.
.
20.
3532
3636
aLGeBra 1
sYsteMatic reVieW 4D - sYsteMatic reVieW 4e
soLutions 169
==
−( ) + ( ) = ( )− + =
100
100 7 100 8 100 12
70 80 121
19. . . .A A
A A00 12
1210
1 15
1 2
18 9
4 75 64
A
A
or
=
=
= .
.
.
20.
3532
3636
Systematic Review 4DSystematicReview 4D1.
2.
3 2 3 3 6
5 3 9 2
A B A B
A
− −( ) = − −− + AA A A
Q X QX Q or QX Q
A B
( ) = − ++( ) = + +
− − − +
15 45 10
3 3 3
2
3.
4. CC A B C
X Y X Y
A B
( ) = + −− = −( ) = ( )+
2
10 25 40 5 2 5 5 8
24 12
5.
6.
;
== +( ) = ( )− − = −− +( ) = −
36 12 2 12 3
14 21 42
7 2 3 7 6
; A B
Q D
Q D
7.
(( )+ =+( ) = ( )+ =
8.
9.
3 4 7
3 4 7 7
22 33 44
11
X XY X
X Y X or X
X
;
22 3 11 4
2 3 42 1
12
7 15 9 5
7 5 9
X
XX
X
Q Q
Q Q
+( ) = ( )+ =
=
=
− = −+ =
10.
++==
− =−( ) = ( )− =
15
12 24
2
30 10 10
10 3 1 10 1
3 1 13
Q
Q
Y
Y
YY
11.
==
=
− =−( ) = ( )− =
=
=
223
56 49 28
7 8 7 7 4
8 7 48 11
118
Y
B
B
BB
B
12.
==
= × = ×= × =
1 38
10 10 1 100 10 10
10 10 100
100
13.
14.
; ;
LCM
.. . .3 100 1 2 100 34
30 120 3430 154
1543
X
XX
X
( ) − ( ) = ( )− =
=
=00
5 215
5 13
4 2 2 6 2 3 10 2 5
2 2
=
= × = × = ×= ×
.
; ; ;
LCM
or
15.
×× × =
( ) −
+ ( ) ( )
3 5 60
60 34
60 16
60 710
4
==
=
− =−( ) = ( )− =
=
=
223
56 49 28
7 8 7 7 4
8 7 48 11
118
Y
B
B
BB
B ==
= × = ×= × =
1 38
10 10 1 100 10 10
10 10 100
100
13.
14.
; ;
LCM
.. . .3 100 1 2 100 34
30 120 3430 154
1543
X
XX
X
( ) − ( ) = ( )− =
=
=00
5 215
5 13
4 2 2 6 2 3 10 2 5
2 2
=
= × = × = ×= ×
.
; ; ;
LCM
or
15.
×× × =
( ) −
+ ( ) = ( )
−
3 5 60
60 34
60 16
60 710
4
15 10 616. R
55 10 4210 87
8710
8 710
8 7
75
05 3
+ ==
=
=
RR
R
R or .
.
.
17.
..
. %
753 5
2525
14
25100
25 25
gum balls
18.
19
= = =
..
20.
40 40 40100
25
125 1 25 125100
1 14
% .
% .
= = =
= = =
==
=
− =−( ) = ( )− =
=
=
223
56 49 28
7 8 7 7 4
8 7 48 11
118
Y
B
B
BB
B ==
= × = ×= × =
1 38
10 10 1 100 10 10
10 10 100
100
13.
14.
; ;
LCM
.. . .3 100 1 2 100 34
30 120 3430 154
1543
X
XX
X
( ) − ( ) = ( )− =
=
=00
5 215
5 13
4 2 2 6 2 3 10 2 5
2 2
=
= × = × = ×= ×
.
; ; ;
LCM
or
15.
×× × =
( ) −
+ ( ) = ( )
−
3 5 60
60 34
60 16
60 710
4
15 10 616. R
55 10 4210 87
8710
8 710
8 7
75
05 3
+ ==
=
=
RR
R
R or .
.
.
17.
..
. %
753 5
2525
14
25100
25 25
gum balls
18.
19
= = =
..
20.
40 40 40100
25
125 1 25 125100
1 14
% .
% .
= = =
= = =
Systematic Review 4ESystematicReview 4E1.
2.
− + −( ) = − − +2 2 3 2 4 62
Q R E Q R E
A 33 3
2 2
4
2 2
2 2 2
+( ) = +− + +( ) = − − −
− + +
B A A B
X Y M XY X MX
A B C
3.
4. (( ) = − − −− = − −( ) = −( )
4 4 4
4 16 18 2 2 8 2 9
2
2 2 2A B C
A B A B5.
6.
;
00 40 100 20 2 20 5
6 12 3 3 2 4
A D A D
Q G Q G
− = −( ) = ( )+ = +( )
;
;7. == ( )− − = − − +( ) = − ( )
× =
3 1
5 15 20 5 3 5 4
56
41
52
5
8.
9.
R T R T;
÷336
41
25
43
1 13
8 10 14
2 4 2 5 7
4 5
× × = =
− = − −− ( ) = − +( )
=
10. C
C
C ++− =
= −
= − −( ) = − −( )
= − −
73 5
35
15 45 30
15 1 15 3 2
1 3
C
C
M
M
M
11.
223 3
1
40 64 48
8 5 8 8 6
13 6
2 16
= −= −
+ =+( ) = ( )
=
=
MM
N
N
N
N
12.
13..
14.
aLGeBra 1
sYsteMatic reVieW 4e - Lesson Practice 5B
soLutions170
3 1
5 15 20 5 3 5 4
56
41
52 336
41
25
43
1 13
8 10 14
2 4 2 5 7
4 5
× × = =
− = − −− ( ) = − +( )
=
10. C
C
C ++− =
= −
= − −( ) = − −( )
= − −
73 5
35
15 45 30
15 1 15 3 2
1 3
C
C
M
M
M
11.
223 3
1
40 64 48
8 5 8 8 6
13 6
2 16
= −= −
+ =+( ) = ( )
=
=
MM
N
N
N
N
12.
13..
14.
63 35 7
7 9 7 5
9 54
4
10 10 1 1
= −( ) = −( )
= −= −= −
= ×
P
P
PP
P
; 0000 10 10 10
10 10 10 1000
1000 5 10
= × ×= × × =
( ) −
;
LCM
.15. Y 000 3 1000 002
500 300 2500 302
3025001
. .( ) = ( )− =
=
=
=
YY
Y
Y 551250
604
3 3 1 4 2 2 12 2 2 3
2
.
; ; ;
LCM
or
16. = × = × = × ×= ×22 3 12
12 113
12 512
12 54
44 5
4 1 3
× =
( ) + ( ) = ( ) −
+
17. K
KKK
K
K or
= −= −
= −
= − −
= =
155 59
595
11 45
11 8
34
75100
.
.18. 775 75
20 20 20100
15
380 3 80 380100
3
=
= = =
= = =
%
% .
% .
19.
20. 445
Lesson Practice 5ASystematicReview5A1.
2.
3.
4.
5.
−( )
− −( )
2 3
2
4 2
3
2
,
,
,,
,
,
−( )
( )
− −( )
2
1
2 3
1
1 5
3
6.
7.
8.
9.
10.
11.
12
see graph
SystematicReview5A1.
2.
3.
4.
5.
−( )
− −( )
2 3
2
4 2
3
2
,
,
,,
,
,
−( )
( )
− −( )
2
1
2 3
1
1 5
3
6.
7.
8.
9.
10.
11.
12
see graph
..
13.
14.
15.
16.
17.
2
1
4
see graph
see graph
geometricaally
18.
19.
positive, negative
the same X coordinaate
20. X, 5
Y
X
F
J
H
SystematicReview5A1.
2.
3.
4.
5.
−( )
− −( )
2 3
2
4 2
3
2
,
,
,,
,
,
−( )
( )
− −( )
2
1
2 3
1
1 5
3
6.
7.
8.
9.
10.
11.
12
see graph
..
13.
14.
15.
16.
17.
2
1
4
see graph
see graph
geometricaally
18.
19.
positive, negative
the same X coordinaate
20. X, 5
21.
22.
23.
24.
1 54320-1-2-3-4-5
1 54320-1-2-3-4-5
1 54320-1-2-3-4-5
1 54320-1-2-3-4-5
21.
22.
23.
24.
1 54320-1-2-3-4-5
1 54320-1-2-3-4-5
1 54320-1-2-3-4-5
1 54320-1-2-3-4-5
Lesson Practice 5BSystematicReview5B1.
2.
3.
4.
5.
2 3
1
1 3
3
2
,
,
,
( )
− −( )
−−( )
−( )
−( )
2
4
2 1
2
5 5
4
6.
7.
8.
9.
10.
11.
12.
,
,
see graph
33
1
4
0 0
13.
14.
15.
16.
17.
18.
see graph
see graph
n
,( )eegative, negative
the same Y coordinate19.
20. Y, −2
aLGeBra 1
Lesson Practice 5B - sYsteMatic reVieW 5c
soLutions 171
1.
2.
3.
4.
5.
2 3
1
1 3
3
2
,
,
,
−−( )
−( )
−( )
2
4
2 1
2
5 5
4
6.
7.
8.
9.
10.
11.
12.
,
,
see graph
33
1
4
0 0
13.
14.
15.
16.
17.
18.
see graph
see graph
n
,( )eegative, negative
the same Y coordinate19.
20. Y, −2
Y
X
QS
R
1.
2.
3.
4.
5.
2 3
1
1 3
3
2
,
,
,
−−( )
−( )
−( )
2
4
2 1
2
5 5
4
6.
7.
8.
9.
10.
11.
12.
,
,
see graph
33
1
4
0 0
13.
14.
15.
16.
17.
18.
see graph
see graph
n
,( )eegative, negative
the same Y coordinate19.
20. Y, −2
1 54320–1–2–3–4–5
1 54320–1–2–3–4–5
1 54320–1–2–3–4–5
1 54320–1–2–3–4–5 21.
22.
23.
24.
Systematic Review 5CSystematicReview5C1.
2.
3.
4.
5 4
2 6
2 1
,
,
,
( )( )−( )
see graph
see graph
see graph
Descartes
posit
5.
6.
7.
8. iive, positive
origin
9.
10.
11.
Y X
X
,
. .100 05 100 1( ) + 22 100 85
5 12 8517 85
5
72 8 328
X
X XXX
YY
( ) = ( )+ =
==
− + ==
.
12.110413
7 2 7 1 13 3 5
7 8 13 8
7
Y
B B B
B B
B
=
− + + −( ) = + +− +( ) = +
−
13.
++ = +=
=
=
− −( ) + = − +
56 13 843 15
4315
2 1315
4 6 2 5 3
BB
B
B
P P14. 66
4 24 2 82 24 8
2 168
3 3 4 2 2 7
− + + =− + =
− = −=
= = ×
P PP
PP
Y
X
F
ED
SystematicReview5C1.
2.
3.
4.
5 4
2 6
2 1
,
,
,
( )( )−( )
see graph
see graph
see graph
Descartes
posit
5.
6.
7.
8. iive, positive
origin
9.
10.
11.
Y X
X
,
. .100 05 100 1( ) + 22 100 85
5 12 8517 85
5
72 8 328
X
X XXX
YY
( ) = ( )+ =
==
− + ==
.
12.110413
7 2 7 1 13 3 5
7 8 13 8
7
Y
B B B
B B
B
=
− + + −( ) = + +− +( ) = +
−
13.
++ = +=
=
=
− −( ) + = − +
56 13 843 15
4315
2 1315
4 6 2 5 3
BB
B
B
P P14. 66
4 24 2 82 24 8
2 168
3 3 4 2 2 7
− + + =− + =
− = −=
= = ×
P PP
PP
9.
10.
11.
Y X
X
,
. .100 05 100 1( ) + 22 100 85
5 12 8517 85
5
72 8 328
X
X XXX
YY
( ) = ( )+ =
==
− + ==
.
12.110413
7 2 7 1 13 3 5
7 8 13 8
7
Y
B B B
B B
B
=
− + + −( ) = + +− +( ) = +
−
13.
++ = +=
=
=
− −( ) + = − +
56 13 843 15
4315
2 1315
4 6 2 5 3
BB
B
B
P P14. 66
4 24 2 82 24 8
2 168
3 3 4 2 2 7
− + + =− + =
− = −=
= = ×
P PP
PP
15. ; ; == = × × × =
( ) − ( ) = ( ) −
7 2 2 3 7 84
84 187
84 14
84 112 21 28
; LCM
Q 773
216 21 476
21 692
69221
32 2021
100
− = −− = −
= −−
=
Q
Q
Q
Q
16. .. . .3 100 06 100 1 25
30 6 12524 125
12
X X
X XX
X
( ) − ( ) = ( )− =
=
= 5524
5 524
116
2 58
2 29
2 2 29
36
X =
× ×
or X 5.21≈
17.
18.
/ \
/ \
// \
/ \
/ \
2 18
2 9
3 3
2 2 3 3× × ×++ +( )
19.
20.
B A
A B C
aLGeBra 1
sYsteMatic reVieW 5D - sYsteMatic reVieW 5e
soLutions172
Systematic Review 5DSystematicReview5D
1.
2.
3.
4.
− −( )−( )
−( )
3 1
0 4
4 2
,
,
,
ssee graph
see graph
see graph
cartesian
ne
5.
6.
7.
8. ggative, positive
same X coordinate9.
10.
11.
X, 3
100 1 3 10 2 7 10 2
13 27 214 2
7
17
−( ) + ( ) = ( )− + =
==
. . . Y
YY
Y
Q12. −− =−( ) = ( )− =− = −
= −−
14 11
17 14 11
17 14 1114 6
61
XQ Q
Q X Q
XX
X44
37
3 7 12 0
3 7 12 04 12
1243
X
D
D DD
D
D
=
−( ) − =− − =
− =
=−
= −
13.
144. 6 9 2 9 8 4 9
36 9 2 9 8 5
4 2 9
2 ÷
÷
( ) × − = − +( )( ) × − = +( )
× −
Y Y
Y Y
Y == +− = +− =− =
= −
=
8 408 9 8 40
32 1732
17
11517
2 2
YY Y
Y
Y
Y
15. ; 44 2 2 7 7
2 2 7 28
28 92
28 54
2814 7 4
= × == × × =
( ) = ( ) + ( )
;
LCM
R 1177
126 35 6858 355835
1 2335
100 35 1
= +=
=
=
( ) +
RR
R
R
P16. . 000 3 2 100 4
35 320 400435 320
32043
.( ) = −( )+ = −
= −
= −
P
P PP
P55
6487
74
75 75 75100
34
113 1
P or P
Y
XF
E
D
Systematic Review 5D 1.
2.
3.
4. see graph
5. see graph
6. see graph
7. cartesian
8. negative, positive
9. same X coordinate
10. X, 3
11.
12.
13.
14.
15.
16.
−3,−1( ) 0,−4( ) −4,2( )
10 −1.3( ) + 10 2.7( ) = 10 .2Y( )−13 + 27 = 2Y
14 = 2Y
7 = Y
17Q = 14XQ = 11Q
Q 17 − 14X( ) = Q 11( )17 −14X = 11
−14X = −6
X = −6−14
= 37
D 3 − 7( ) −12 = 0
3D − 7D −12 = 0
−4D = 12
D = 12−4
= −3
62 ÷ 9( ) × 2 − 9Y = 8 Y − 4 + 9( )36 ÷ 9( ) × 2 − 9Y = 8 Y + 5( )4 × 2 − 9Y = 8Y + 40
8 − 9Y = 8Y + 40
−32 = 17Y
−3217
= Y = −11517
2 = 2; 4 = 2 × 2; 7 = 7
LCM = 2 × 2 × 7 = 28
14 28( ) 9
2=7 28( ) 5
4R +4 28( )17
7
126 = 35R + 68
58 = 35R
5835
= R = 12335
100 .35P( ) +100 3.2( ) = 100 −4P( )
SystematicReview5D1.
2.
3.
4.
− −( )−( )
−( )
3 1
0 4
4 2
,
,
,
ssee graph
see graph
see graph
cartesian
ne
5.
6.
7.
8. ggative, positive
same X coordinate9.
10.
11.
X, 3
100 1 3 10 2 7 10 2
13 27 214 2
7
17
−( ) + ( ) = ( )− + =
==
. . . Y
YY
Y
Q12. −− =−( ) = ( )− =− = −
= −−
14 11
17 14 11
17 14 1114 6
61
XQ Q
Q X Q
XX
X44
37
3 7 12 0
3 7 12 04 12
1243
X
D
D DD
D
D
=
−( ) − =− − =
− =
=−
= −
13.
144. 6 9 2 9 8 4 9
36 9 2 9 8 5
4 2 9
2 ÷
÷
( ) × − = − +( )( ) × − = +( )
× −
Y Y
Y Y
Y == +− = +− =− =
= −
=
8 408 9 8 40
32 1732
17
11517
2 2
YY Y
Y
Y
Y
15. ; 44 2 2 7 7
2 2 7 28
28 92
28 54
2814 7 4
= × == × × =
( ) = ( ) + ( )
;
LCM
R 1177
126 35 6858 355835
1 2335
100 35 1
= +=
=
=
( ) +
RR
R
R
P16. . 000 3 2 100 4
35 320 400435 320
32043
.( ) = −( )+ = −
= −
= −
P
P PP
P55
6487
74
75 75 75100
34
113 1
P or P
6 9 2 9 8 4 9
36 9 2 9 8 5
4 2 9× −
Y Y
Y Y
Y == +− = +− =− =
= −
=
8 408 9 8 40
32 1732
17
11517
2 2
YY Y
Y
Y
Y
15. ; 44 2 2 7 7
2 2 7 28
28 92
28 54
2814 7 4
= × == × × =
( ) = ( ) + ( )
;
LCM
R 1177
126 35 6858 355835
1 2335
100 35 1
= +=
=
=
( ) +
RR
R
R
P16. . 000 3 2 100 4
35 320 400435 320
32043
.( ) = −( )+ = −
= −
= −
P
P PP
P55
6487
74
75 75 75100
34
113 1
P or P= − −
= = =
=
.
% .
%
≈
17.
18. ..
. %
13 113100
1 13100
25
40100
40 40
= =
= = =
+
19.
20. AB AB
Systematic Review 5E SystematicReview5E1.
2.
3.
4.
3 3
4 2
5 5
,
,
,
( )−( )
−( )seee graph
see graph
see graph
negat
5.
6.
7.
8.
analytic
iive, negative
same X coordinate9.
10. X, −2
Systematic Review 5E 1.
2.
3.
4. see graph
5. see graph
6. see graph
7. analytic
8. negative, negative
9. same X coordinate
10.
11.
12.
13.
3,3( ) 4,−2( ) −5,5( )
Y
X
F
D
E
X, −2
100 1.08V( ) = 100 .7( ) −100 .24( )108V = 70 − 24
108V = 46
V = 46108
= 2354
9X2M = 10X2 −19X2
X2 9M( ) = X2 10 − 19( )9M = 10 − 19
9M = −9
M = −99
= −1
11− 4( )2
÷ 7 − 3 − 9 = 14 R + 3R − 2R + 1( )
SystematicReview5E1.
2.
3.
4.
3 3
4 2
5 5
,
,
,
( )−( )
−( )seee graph
see graph
see graph
negat
5.
6.
7.
8.
analytic
iive, negative
same X coordinate9.
10. X, −210.
11.
X
V
V
,
. . .
−
( ) = ( ) − ( )= −
2
100 1 08 100 7 100 24
108 70 244108 46
46108
2354
9 10 19
9
2 2 2
2 2
V
V
X M X X
X M X
=
= =
= −( ) =
12.
110 19
9 10 199 9
991
11 4 7 3 92
−( )= −= −
= −
= −
−( ) − − =
MM
M
M
13. ÷ 114 3 2 1
7 7 6 14 2 1
49 7 6 28 147 6
2
R R R
R
R
+ − +( )− − = +( )− = +− =
÷
÷228 14
1 28 1413 28
1328
6 8 4 3 1
RRR
R
Y
aLGeBra 1
sYsteMatic reVieW 5e - Lesson Practice 6a
soLutions 173
10.
11.
X
V
V
,
. . .
−
( ) = ( ) − ( )= −
2
100 1 08 100 7 100 24
108 70 244108 46
46108
2354
9 10 19
9
2 2 2
2 2
V
V
X M X X
X M X
=
= =
= −( ) =
12.
110 19
9 10 199 9
991
11 4 7 3 92
−( )= −= −
= −
= −
−( ) − − =
MM
M
M
13. ÷ 114 3 2 1
7 7 6 14 2 1
49 7 6 28 147 6
2
R R R
R
R
+ − +( )− − = +( )− = +− =
÷
÷228 14
1 28 1413 28
1328
6 8 4 3 1
RRR
R
Y
+= +
− =
= −
− +( ) =14. 00 1 7 5 4
6 8 4 3 11 6
6 4 3 1
2
2
+( ) − − +( )
− −[ ] = − −[ ] =
Y
Y 221 6
24 6 3 115
24 6 3456 321
3216
53
−[ ]− = [ ]− =− =
=−
= −
Y
YY
Y
Y 112
2 2 7 7 8 2 2 2
2 2 2 7 56
56 258
7
15. = = = × ×= × × × =
( )
; ; ;
LCM
−− ( ) = ( )− =
=
=
=
8 2856 117
56 32
175 88 8487 848784
1 12
D
DD
D
D88
1000 1 203 1000 9 1000 6
1203 900
16. −( ) + ( ) = −( )− +
. . .H
H == −− = −
= −−
=
6001203 1500
15001203
1 2971203
1
H
H
H or H ≈ ..
.
.
.
25
125
8 1 0008
2016
4040
17.
or 113
666
3 2 0001 8
2018
2018
18. .
.
or ..
.
.
.
.
67
6
5 3 03 0
22
9 2 001 8
2018
56 117
56 32
175 88 8487 848784
1 12
D
DD
D
D88
1000 1 203 1000 9 1000 6
1203 900
16. −( ) + ( ) = −( )− +
. . .H
H == −− = −
= −−
=
6001203 1500
15001203
1 2971203
1
H
H
H or H ≈ ..
.
.
.
25
125
8 1 0008
2016
4040
17.
or 113
666
3 2 0001 8
2018
2018
18. .
.
or ..
.
.
.
.
67
6
5 3 03 0
22
9 2 001 8
2018
19.
20.
or .22
Lesson Practice 6ALessonPractice 6A1.
2.
hours loaves0 21 52 83 11
on thee graph
on th
3.
4.
5.
L H
hours rackets
= +
−−
3 2
0 31 12 13 3
ee graph
on the
6.
7.
8.
R H
hours steaks
= −2 3
0 11 52 93 13
ggraph
on the graph
A
9.
10.
11.
12.
S H
X Y
= +
−
4 1
0 11 12 33 5
nnswers will vary. Your problem
should start witth a negative
amount.
LessonPractice 6A1.
2.
hours loaves0 21 52 83 11
on thee graph
on th
3.
4.
5.
L H
hours rackets
= +
−−
3 2
0 31 12 13 3
ee graph
on the
6.
7.
8.
R H
hours steaks
= −2 3
0 11 52 93 13
ggraph
on the graph
A
9.
10.
11.
12.
S H
X Y
= +
−
4 1
0 11 12 33 5
nnswers will vary. Your problem
should start witth a negative
amount.
loaves
hours
aLGeBra 1
Lesson Practice 6a - Lesson Practice 6B
soLutions174
LessonPractice 6A1.
2.
hours loaves0 21 52 83 11
on thee graph
on th
3.
4.
5.
L H
hours rackets
= +
−−
3 2
0 31 12 13 3
ee graph
on the
6.
7.
8.
R H
hours steaks
= −2 3
0 11 52 93 13
ggraph
on the graph
A
9.
10.
11.
12.
S H
X Y
= +
−
4 1
0 11 12 33 5
nnswers will vary. Your problem
should start witth a negative
amount.
rackets
hours
LessonPractice 6A1.
2.
hours loaves0 21 52 83 11
on thee graph
on th
3.
4.
5.
L H
hours rackets
= +
−−
3 2
0 31 12 13 3
ee graph
on the
6.
7.
8.
R H
hours steaks
= −2 3
0 11 52 93 13
ggraph
on the graph
A
9.
10.
11.
12.
S H
X Y
= +
−
4 1
0 11 12 33 5
nnswers will vary. Your problem
should start witth a negative
amount.
steaks
hours
LessonPractice 6A1.
2.
hours loaves0 21 52 83 11
on thee graph
on th
3.
4.
5.
L H
hours rackets
= +
−−
3 2
0 31 12 13 3
ee graph
on the
6.
7.
8.
R H
hours steaks
= −2 3
0 11 52 93 13
ggraph
on the graph
A
9.
10.
11.
12.
S H
X Y
= +
−
4 1
0 11 12 33 5
nnswers will vary. Your problem
should start witth a negative
amount.
Y
X
LessonPractice 6A1.
2.
hours loaves0 21 52 83 11
on thee graph
on th
3.
4.
5.
L H
hours rackets
= +
−−
3 2
0 31 12 13 3
ee graph
on the
6.
7.
8.
R H
hours steaks
= −2 3
0 11 52 93 13
ggraph
on the graph
A
9.
10.
11.
12.
S H
X Y
= +
−
4 1
0 11 12 33 5
nnswers will vary. Your problem
should start witth a negative
amount.
Lesson Practice 6BLessonPractice 6B1. weeks centimeters
0 61 42 23 0
−−−
22.
3.
4.
5.
on the graph
o
C W
hours fish
= −
−−
2 6
0 51 22 13 4
nn the graph
seconds meters
6.
7.
8
F H= −
−−−
3 5
0 51 32 13 1
..
9.
10.
11.
on the graph
on the
M S
X Y
= −
−−
2 5
0 41 12 23 5
ggraph
Answers will vary. Your problem
should
12.
sstart with a negative
amount.
cm
days
fish
hours
meters
seconds
Lesson Practice 6B 1.
2. on the graph
3. C = 2W – 6
4.
5. on the graph
6. F = 3H – 5
7.
8. on the graph
weeks centimeters
0 −6
1 −4
2 −2
3 0
hours fish
0 −5
1 −2
2 1
3 4
seconds meters
0 −5
1 −3
2 −1
3 1
LessonPractice 6B1. weeks centimeters
0 61 42 23 0
−−−
22.
3.
4.
5.
on the graph
o
C W
hours fish
= −
−−
2 6
0 51 22 13 4
nn the graph
seconds meters
6.
7.
8
F H= −
−−−
3 5
0 51 32 13 1
..
9.
10.
11.
on the graph
on the
M S
X Y
= −
−−
2 5
0 41 12 23 5
ggraph
Answers will vary. Your problem
should
12.
sstart with a negative
amount.
cm
days
fish
hours
meters
seconds
Lesson Practice 6B 1.
2. on the graph
3. C = 2W – 6
4.
5. on the graph
6. F = 3H – 5
7.
8. on the graph
9. M = 2S – 5
weeks centimeters
0 −6
1 −4
2 −2
3 0
hours fish
0 −5
1 −2
2 1
3 4
seconds meters
0 −5
1 −3
2 −1
3 1
LessonPractice 6B1. weeks centimeters
0 61 42 23 0
−−−
22.
3.
4.
5.
on the graph
o
C W
hours fish
= −
−−
2 6
0 51 22 13 4
nn the graph
seconds meters
6.
7.
8
F H= −
−−−
3 5
0 51 32 13 1
..
9.
10.
11.
on the graph
on the
M S
X Y
= −
−−
2 5
0 41 12 23 5
ggraph
Answers will vary. Your problem
should
12.
sstart with a negative
amount.
aLGeBra 1
Lesson Practice 6B - sYsteMatic reVieW 6c
soLutions 175
meters
seconds
Y
X
8. on the graph
9. M = 2S – 5
10.
11. on the graph
12. Answers will vary. Your problem should start with a negative amount.
seconds meters
0 −5
1 −3
2 −1
3 1
X Y
0 −4
1 −1
2 2
3 5
weeks centimeters0 61 42 23 0
−−−
22.
3.
4.
5.
on the graph
o
C W
hours fish
= −
−−
2 6
0 51 22 13 4
nn the graph
seconds meters
6.
7.
8
F H= −
−−−
3 5
0 51 32 13 1
..
9.
10.
11.
on the graph
on the
M S
X Y
= −
−−
2 5
0 41 12 23 5
ggraph
Answers will vary. Your problem
should
12.
sstart with a negative
amount.
meters
seconds
Y
X
on the graph
9. M = 2S – 5
10.
11. on the graph
12. Answers will vary. Your problem should start with a negative amount.
X Y
0 −4
1 −1
2 2
3 5
weeks centimeters0 61 42 23 0
−−−
22.
3.
4.
5.
on the graph
o
C W
hours fish
= −
−−
2 6
0 51 22 13 4
nn the graph
seconds meters
6.
7.
8
F H= −
−−−
3 5
0 51 32 13 1
..
9.
10.
11.
on the graph
on the
M S
X Y
= −
−−
2 5
0 41 12 23 5
ggraph
Answers will vary. Your problem
should
12.
sstart with a negative
amount.
Systematic Review 6C1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
days speeches
0 1
1 3
2 5
3 7
on the graph
2; 1; S 2D 1
years masterpieces
0 0
1 2
2 4
3 6
on the graph
M 2Y
quadrant 1
quadrant 2
on the graph
on the graph
63A 81 72
9 7A 9 9 8
7A 9 87A 17
A 177
A 2 37
48 54X 36
6 8 9X 6 6
8 9X 69X 2
X 29
5 5 3 100 10X 3X 2X
5 5 5 5 3 100 5X
25 25 3 100 5X
50 3 100 5X150 100 5X
50 5X505
X
X 10
100 .01 100 .1 100 .5 100 2Y
1 10 50 200Y41 200Y
Y 41200
or .205
A 2A
A 5A
A XA
2 5 XX 3
6 52
X 6 23
X 6 116
15X 4X 1119X 11
X 1119
or X ≈ .58
.625
8 5.000 4 8
20 16
40 40
X X Y 2Q X XY 2QX
A
B
( ) ( )
( ) ( )
( )( ) ( ) ( )
( ) ( )
= +
=
− =− =− =
=
=
=
+ =+ =+ =
= −
= −
− − −
× + = − −
− × − − − × + =− − × + =
− × + =− + =
− =− =
= −
− + =− + =
=
=
− =
− == −
+ =
+ ==
=
+ + = + +
SystematicReview 6C
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
days speeches
0 1
1 3
2 5
3 7
on the graph
2; 1; S 2D 1
years masterpieces
0 0
1 2
2 4
3 6
on the graph
M 2Y
quadrant 1
quadrant 2
on the graph
on the graph
63A 81 72
9 7A 9 9 8
7A 9 87A 17
A 177
A 2 37
48 54X 36
6 8 9X 6 6
8 9X 69X 2
X 29
5 5 3 100 10X 3X 2X
5 5 5 5 3 100 5X
25 25 3 100 5X
50 3 100 5X150 100 5X
50 5X505
X
X 10
100 .01 100 .1 100 .5 100 2Y
1 10 50 200Y41 200Y
Y 41200
or .205
A 2A
A 5A
A XA
2 5 XX 3
6 52
X 6 23
X 6 116
15X 4X 1119X 11
X 1119
or X ≈ .58
.625
8 5.000 4 8
20 16
40 40
X X Y 2Q X XY 2QX
A
B
2 2
1 1 1
3 2 1
2
( ) ( ) ( )
( ) ( ) ( )
[ ]
( ) ( )
( ) ( )
( )( ) ( ) ( )
( ) ( )( ) ( )
= +
=
− =− =− =
=
=
=
+ =+ =+ =
= −
= −
− − −
× + = − −
− × − − − × + =− − × + =
− × + =− + =
− =− =
= −
− + =− + =
=
=
− =
− == −
+ =
+ ==
=
+ + = + +
speeches/Masterpieces
days
/years
#5
#7#8
#10#2
#9
on the graph
6. M = 2Y
7. quadrant 1
8. quadrant 2
9. on the graph
10. on the graph
11.
12.
13.
14.
15.
16.
63A − 8A = 72
9 7A − 9( ) = 9 8( )7A − 9 = 8
7A = 17
A = 177
= 237
48 + 54X = 36
6 8 + 9X( ) = 6 6( )8 + 9X = 6
9X = −2
X = −29
−52 − 5( )2��
��×3+100 = 5X
− 5 × 5( ) − 5( ) 5( )�� �� × 3 + 100 = 5X
−25 − 25[ ] × 3 + 100 = 5X
−50 × 3 + 100 = 5X
−150 + 100 = 5X
−50 = 5X−505
= X= −10
100 .10( ) − 100 .1( ) + 100 .5( ) = 100 2Y( )1− 10 + 50 = 200Y
41= 200Y
Y = 41200
�or�.205
1 A( ) 2
A−1 A( ) 5
A=1 A( ) X
A2 − 5 = X
−3 = X
3 6( ) 5
2X +2 6( ) 2
3X =1 6( )11
6
15X + 4X = 11
19X = 11
X = 1119
�or�.58� rounded( )��� � .6258�5.000
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
days speeches
0 1
1 3
2 5
3 7
on the graph
2; 1; S 2D 1
years masterpieces
0 0
1 2
2 4
3 6
on the graph
M 2Y
quadrant 1
quadrant 2
on the graph
on the graph
63A 81 72
9 7A 9 9 8
7A 9 87A 17
A 177
A 2 37
48 54X 36
6 8 9X 6 6
8 9X 69X 2
X 29
5 5 3 100 10X 3X 2X
5 5 5 5 3 100 5X
25 25 3 100 5X
50 3 100 5X150 100 5X
50 5X505
X
X 10
100 .01 100 .1 100 .5 100 2Y
1 10 50 200Y41 200Y
Y 41200
or .205
A 2A
A 5A
A XA
2 5 XX 3
6 52
X 6 23
X 6 116
15X 4X 1119X 11
X 1119
or X ≈ .58
.625
8 5.000 4 8
20 16
40 40
X X Y 2Q X XY 2QX
A
B
2 2
1 1 1
3 2 1
2
( ) ( ) ( )
( ) ( ) ( )
[ ]
( ) ( )
( ) ( )
( )( ) ( ) ( )
( ) ( )( ) ( )
= +
=
− =− =− =
=
=
=
+ =+ =+ =
= −
= −
− − −
× + = − −
− × − − − × + =− − × + =
− × + =− + =
− =− =
= −
− + =− + =
=
=
− =
− == −
+ =
+ ==
=
+ + = + +
aLGeBra 1
sYsteMatic reVieW 6c - sYsteMatic reVieW 6D
soLutions176
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
0 0
1 2
2 4
3 6
on the graph
M 2Y
quadrant 1
quadrant 2
on the graph
on the graph
63A 81 72
9 7A 9 9 8
7A 9 87A 17
A 177
A 2 37
48 54X 36
6 8 9X 6 6
8 9X 69X 2
X 29
5 5 3 100 10X 3X 2X
5 5 5 5 3 100 5X
25 25 3 100 5X
50 3 100 5X150 100 5X
50 5X505
X
X 10
100 .01 100 .1 100 .5 100 2Y
1 10 50 200Y41 200Y
Y 41200
or .205
A 2A
A 5A
A XA
2 5 XX 3
6 52
X 6 23
X 6 116
15X 4X 1119X 11
X 1119
or X ≈ .58
.625
8 5.000 4 8
20 16
40 40
X X Y 2Q X XY 2QX
A
B
2 2
1 1 1
3 2 1
2
( ) ( ) ( )
( ) ( ) ( )
( )
= +
=
− =− =− =
=
=
=
+ =+ =+ =
= −
= −
− − −
× + = − −
− × − − − × + =− − × + =
− × + =− + =
− =− =
= −
− + =− + =
=
=
− =
− == −
+ =
+ ==
=
+ + = + +
Systematic Review 6DSystematicReview 6D1.
2.
hours pages
0 0
1 3
2 6
3 9
on thee graph
on
3.
4.
5.
3 0 3
0 3
1 5
2 7
3 9
; ; P H
customer eggs
=
tthe graph
quadrant 2
quadrant 4
6.
7.
8.
E C= +2 3
SystematicReview 6D1.
2.
hours pages
0 0
1 3
2 6
3 9
on thee graph
on
3.
4.
5.
3 0 3
0 3
1 5
2 7
3 9
; ; P H
customer eggs
=
tthe graph
quadrant 2
quadrant 4
6.
7.
8.
E C= +2 3
on the graph
6. E = 2C + 3
7. quadrant 2
8. quadrant 4
9. on the graph
10. on the graph
11.
12.
13.
14.
15.
16.
−6 Y − 5 + 9( ) + 7 2Y + 9( ) = −1
−6 Y + 4( ) + 14Y + 63 = −1
−6Y − 24 + 14Y + 63 = −1
8Y + 39 = −18Y = −40
Y = −408
= −5
3X + 3 − X − 8 + 5X + 12 = 4X − 12 − 6X + 10
7X + 7 = −2X − 2
9X = −9
X = −99
= −1
−5R + 92 − 32 + 13 = 7R + 5R
−5R + 81− 9 + 13 = 12R
72 + 13 = 12R + 5R
72 + 13 = 17R
85 = 17R
R = 8517
= 5
8 − −2( )�� ��2
= 10X
8 + 2[ ]2= 10X
102 = 10X
100 = 10X
X = 10010
1 2A( ) Y
2A−2 2A( ) 4
A=1 2A( ) 1
2A
Y − 8 = 1
Y = 9
8 40( )13
5D −5 40( ) 3
8D =4 40( ) 47
10
104D − 15D = 188
89D = 188
D = 18889
= 21089
�or�2.11� rounded( )
pages/eggs
hours/customers
#8
#7
#10
#2
#5 #9
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
on the graph
on the graph
6 Y 5 9 7 2Y 9 1
6 Y 4 14Y 63 1
6Y 24 14Y 63 18Y 39 1
8Y 40
Y 408
Y 5
3X 3 X 8 5X 12 4X 12 6X 107X 7 2X 2
9X 9
X 99
X 1
5R 9 3 13 7R 5R
5R 81 9 13 12R
72 13 12R 5R72 13 17R
85 17R
R 8517
R 5
8 2 10X
8 2 10X
10 10X100 10X
X 10010
X 10
2A Y2A
2A 4A
2A 12A
Y 8 1Y 9
40 135
D 40 38
D 40 4710
104D 15D 18889D 188
D 18889
D 2 1089
or D ≈ 2.11
.9166
12 11.0000 10 8
20 12
80 72
80
or .916
X Y 4X Y BX Y 0
X Y 1 4 B 0
X Y 1 4 B
X Y
0
X Y1 4 B 0
3 B 0B 3
B
A A B 2AB A AB 2A B
2 2
2
2
2
1 2 1
8 5 4
2 2 2
2
2
2 2
2 2
( ) ( ) ( )
( ) ( ) ( )
[ ]
( ) ( )( )
( )
− − + + + = −− + + + = −− − + + = −
+ = −= −
= −
= −
+ − − + + = − − ++ = − −
= −
= −
= −
− + − + = +− + − + =
+ = ++ =
=
=
=
− − =
+ =
==
=
=
− =
− ==
− =
− ==
=
=
− + =− + =
− + =
− + =− + =
=
− + = − +
aLGeBra 1
sYsteMatic reVieW 6D - sYsteMatic reVieW 6e
soLutions 177
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
on the graph
on the graph
6 Y 5 9 7 2Y 9 1
6 Y 4 14Y 63 1
6Y 24 14Y 63 18Y 39 1
8Y 40
Y 408
Y 5
3X 3 X 8 5X 12 4X 12 6X 107X 7 2X 2
9X 9
X 99
X 1
5R 9 3 13 7R 5R
5R 81 9 13 12R
72 13 12R 5R72 13 17R
85 17R
R 8517
R 5
8 2 10X
8 2 10X
10 10X100 10X
X 10010
X 10
2A Y2A
2A 4A
2A 12A
Y 8 1Y 9
40 135
D 40 38
D 40 4710
104D 15D 18889D 188
D 18889
D 2 1089
or D ≈ 2.11
.9166
12 11.0000 10 8
20 12
80 72
80
or .916
X Y 4X Y BX Y 0
X Y 1 4 B 0
X Y 1 4 B
X Y
0
X Y1 4 B 0
3 B 0B 3
B
A A B 2AB A AB 2A B
2 2
2
2
2
1 2 1
8 5 4
2 2 2
2
2
2 2
2 2
( ) ( ) ( )
( ) ( ) ( )
[ ]
( )
( )
( )( )
( )
− − + + + = −− + + + = −− − + + = −
+ = −= −
= −
= −
+ − − + + = − − ++ = − −
= −
= −
= −
− + − + = +− + − + =
+ = ++ =
=
=
=
− − =
+ =
==
=
=
− =
− ==
− =
− ==
=
=
− + =− + =
− + =
− + =− + =
=
− + = − +
Systematic Review 6ESystematicReview 6E1.
2.
3.
3 1
1 3
;
;
on the graph
BB M
X Y
= +3
0 21 32 43 5
4.
5.
6.
on the graph
answers will vvary
Y axis
X axis
on the graph
on the gr
7.
8.
9.
10. aaph
11. 4 7 15
4 7 15
4 7 154 22
224
AB A A
A B A
BB
B
− =−( ) = ( )− =
=
= ==
+ − −( ) ( )
5 12
7 6 2 4 3 4 8 9 2
7 2 9 2
3
0 21 32 43 5
4.
5.
6.
on the graph
answers will vvary
Y axis
X axis
on the graph
on the gr
7.
8.
9.
10. aaph
11. 4 7 15
4 7 15
4 7 154 22
224
AB A A
A B A
BB
B
− =−( ) = ( )− =
=
= ==
+ − −( ) = − − − +( )− +( ) = − −
5 12
7 6 2 4 3 4 8 9 2
7 2 9 2
212. B B B B
B B 1177 14 18 153
11 14 15311 167
16711
( )− + = − −
+ = −= −
= −
B BB
B
B
BB
G G G G
G
= −
− +( ) + − = + − −( )− ( ) + −
15 211
3 3 5 3 12 18 5 4
3 8
13.
99 18 5 20
24 9 13 2037 29
2937
100 1
= − −− + = −
− = −
=
−
G G
G GG
G
14. .. . .2 100 07 100 3
120 7 307 150
1507
( ) + ( ) = ( )− + =
=
=
=
X
XX
X
X 221 37
21 43
40 310
40 85
40 58
1
4 8 5
.or X
M
≈
15. ( ) − ( ) = ( ) −
22 64 2552 25
5225
2 225
2 08
10
− = −− = −
= −−
= =
MM
M
M or M .
16. 990 59
90 176
90 710
50 255 6350 318
3
15 9( ) − ( ) = ( )− =
=
=
X
XX
X 11850
6 925
6 36
285 29
7 2 0
X or X
or
= = .
. .
.
17. ≈
000
14
60
56
40
35
% .
5
35 35 35100
720
4 2 5
Y
X
#7
#8
#2
#5
#10
5. on the graph
6. answers will vary
7. Y axis
8. X axis
9. on the graph
10. on the graph
11.
12.
13.
14.
15.
16.
X Y
0 2
1 3
2 4
3 5
4AB −7A = 15A
A 4B −7( ) = A 15( )4B −7 = 15
4B = 22
B = 224
= 512
7 B + 6 − 2B − 4( ) = 32 −4B − 8 − 9 + 2B( )7 −B + 2( ) = 9 −2B −17( )−7B +14 = −18B −153
11B +14 = −153
11B = −167
B = −16711
= −15 211
�or�−15.18
−3 3G +5G( ) + 3−12 = 18G +5 −G − 4( )−3 8G( ) + −9 = 18G −5G − 20
−24G + 9 = 13G − 20
−37G = −29
G = −29−37
= 2937
100 −1.2( ) +100 .07X( ) = 100 .3( )−120 +7X = 30
7X = 150
X = 1507
= 2137
�or�21.43� rounded( )
4 40( ) 3
10−8 40( ) 8
5=5 40( ) −5
8M
12− 64 = −25M
−52 = −25M
M = −52−25
= 2 225
�or�2.08
10 90( ) 5
9X −15 90( )17
6=9 90( ) 7
10
50X
#9
SystematicReview 6E1.
2.
3.
3 1
1 3
;
;
on the graph
BB M
X Y
= +3
0 21 32 43 5
4.
5.
6.
on the graph
answers will vvary
Y axis
X axis
on the graph
on the gr
7.
8.
9.
10. aaph
11. 4 7 15
4 7 15
4 7 154 22
224
AB A A
A B A
BB
B
− =−( ) = ( )− =
=
= ==
+ − −( ) = − − − +( )− +( ) = − −
5 12
7 6 2 4 3 4 8 9 2
7 2 9 2
212. B B B B
B B 1177 14 18 153
11 14 15311 167
16711
( )− + = − −
+ = −= −
= −
B BB
B
B
BB
G G G G
G
= −
− +( ) + − = + − −( )− ( ) + −
15 211
3 3 5 3 12 18 5 4
3 8
13.
99 18 5 20
24 9 13 2037 29
2937
100 1
= − −− + = −
− = −
=
−
G G
G GG
G
14. .. . .2 100 07 100 3
120 7 307 150
1507
( ) + ( ) = ( )− + =
=
=
=
X
XX
X
X 221 37
21 43
40 310
40 85
40 58
1
4 8 5
.or X
M
≈
15. ( ) − ( ) = ( ) −
22 64 2552 25
5225
2 225
2 08
10
− = −− = −
= −−
= =
MM
M
M or M .
16. 990 59
90 176
90 710
50 255 6350 318
3
15 9( ) − ( ) = ( )− =
=
=
X
XX
X 11850
6 925
6 36
285 29
7 2 0
X or X
or
aLGeBra 1
sYsteMatic reVieW 6e - sYsteMatic reVieW 7c
soLutions178
99 18 5 20
24 9 13 2037 29
2937
100 1
= − −− + = −
− = −
=
−14. .. . .2 100 07 100 3
120 7 307 150
1507
( ) + ( ) = ( )− + =
=
=
=
X
XX
X
X 221 37
21 43
40 310
40 85
40 58
1
4 8 5
.or X
M
≈
15. ( ) − ( ) = ( ) −
22 64 2552 25
5225
2 225
2 08
10
− = −− = −
= −−
= =
MM
M
M or M .
16. 990 59
90 176
90 710
50 255 6350 318
3
15 9( ) − ( ) = ( )− =
=
=
X
XX
X 11850
6 925
6 36
285 29
7 2 0
X or X
or
= = .
. .
.
17. ≈
000
14
60
56
40
35
% .
5
35 35 35100
720
4 2 5
18.
19.
= = =
−( ) −( ) ⋅( )N ÷
220. 3 2 7N N N− + +
Lesson Practice 7ALessonPractice 7A.11.
2.
3.
intercept
up; over
negattive
negative; m 6–2
positive; m 84
p
4.
5.
6.
= =
= =
–3
2
oositive; m 77
m 63
= =
=−
=
1
27.
8.
negative
negative
; –
;; –
;
m 33
m 31
=−
=
= =
1
39. positive
Lesson Practice 7BLessonPractice 7A.21.
2.
3.
4.
4
3
slope
negative; m = 228
35
positive; 46
−= −
=
= =
14
23
5.
6.
7.
positive m
m
ne
;
ggative m
negative m
positi
;
;–
=−
= −
= = −
12
12
26
13
8.
9. vve m; = =68
34
Systematic Review 7C1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
3
down
m 64
32
; b 2
Y 32
X 2
m –13
13
; b 1
Y 13
X 1
m 34
; b 0
Y 34
X
m 24
12
;b 1
Y 12
X 1
7 3 4 9 ÷3
4 16 9 ÷27
64 9 ÷27
55÷27 2 127
4 2 8 7 5 19
6 64 35 19
6 64 35 19 54
13 5÷10 169 5÷10
169 .5 169.5
5 9 2 6 7 2 3 5 7 6 7 8 3
35 42 24 17
2X 5 X 132X X 13 5
3X 18X 6
Y 14 3Y 0Y 3Y 14
2Y 14Y 7
3 12
B 23
5 14
56
B
12 72
B 23
12 214
56
B
42B 8 63 10B8 63 10B 42B
55 52B5552
B
B 5552
or –1 352
2.7T 1.09 5.3 .6T
100 2.7T 1.09 100 5.3 .6T
270T 109 530 60T270T 60T 530 109
330T 421
T 421330
or 1 91330
2 3
2
2
3
[ ]
[ ]
[ ] [ ]
( )
( )
( ) ( ) ( ) ( )
−
= = = −
= −
= = − =
= − +
= =
=
= = = −
= −
− × − =× − =
− =
=
− − + − × + =− + − + =
+ − + =
+ = += + =
− − + ⋅ = − + ⋅= − + =
− = − ++ = +
==
+ − =− = −− = −
=
− + = +
− +
= +
− + = +− = +− =
− =
= −
+ = −+ = −+ = −+ = −
=
=
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
3
down
m 64
32
; b 2
Y 32
X 2
m –13
13
; b 1
Y 13
X 1
m 34
; b 0
Y 34
X
m 24
12
;b 1
Y 12
X 1
7 3 4 9 ÷3
4 16 9 ÷27
64 9 ÷27
55÷27 2 127
4 2 8 7 5 19
6 64 35 19
6 64 35 19 54
13 5÷10 169 5÷10
169 .5 169.5
5 9 2 6 7 2 3 5 7 6 7 8 3
35 42 24 17
2X 5 X 132X X 13 5
3X 18X 6
Y 14 3Y 0Y 3Y 14
2Y 14Y 7
3 12
B 23
5 14
56
B
12 72
B 23
12 214
56
B
42B 8 63 10B8 63 10B 42B
55 52B5552
B
B 5552
or –1 352
2.7T 1.09 5.3 .6T
100 2.7T 1.09 100 5.3 .6T
270T 109 530 60T270T 60T 530 109
330T 421
T 421330
or 1 91330
2 3
2
2
3
[ ]
[ ]
[ ] [ ]
( )
( )
( ) ( ) ( ) ( )
−
= = = −
= −
= = − =
= − +
= =
=
= = = −
= −
− × − =× − =
− =
=
− − + − × + =− + − + =
+ − + =
+ = += + =
− − + ⋅ = − + ⋅= − + =
− = − ++ = +
==
+ − =− = −− = −
=
− + = +
− +
= +
− + = +− = +− =
− =
= −
+ = −+ = −+ = −+ = −
=
=
-5 -4 -3 -2 -1 0 1 2 3 4 511.
12.-5 -4 -3 -2 -1 0 1 2 3 4 5
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
3
down
m 64
32
; b 2
Y 32
X 2
m –13
13
; b 1
Y 13
X 1
m 34
; b 0
Y 34
X
m 24
12
;b 1
Y 12
X 1
7 3 4 9 ÷3
4 16 9 ÷27
64 9 ÷27
55÷27 2 127
4 2 8 7 5 19
6 64 35 19
6 64 35 19 54
13 5÷10 169 5÷10
169 .5 169.5
5 9 2 6 7 2 3 5 7 6 7 8 3
35 42 24 17
2X 5 X 132X X 13 5
3X 18X 6
Y 14 3Y 0Y 3Y 14
2Y 14Y 7
3 12
B 23
5 14
56
B
12 72
B 23
12 214
56
B
42B 8 63 10B8 63 10B 42B
55 52B5552
B
B 5552
or –1 352
2.7T 1.09 5.3 .6T
100 2.7T 1.09 100 5.3 .6T
270T 109 530 60T270T 60T 530 109
330T 421
T 421330
or 1 91330
2 3
2
2
3
[ ]
[ ]
[ ] [ ]
( )
( )
( ) ( ) ( ) ( )
−
= = = −
= −
= = − =
= − +
= =
=
= = = −
= −
− × − =× − =
− =
=
− − + − × + =− + − + =
+ − + =
+ = += + =
− − + ⋅ = − + ⋅= − + =
− = − ++ = +
==
+ − =− = −− = −
=
− + = +
− +
= +
− + = +− = +− =
− =
= −
+ = −+ = −+ = −+ = −
=
=
aLGeBra 1
sYsteMatic reVieW 7c - sYsteMatic reVieW 7D
soLutions 179
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
3
down
m 64
32
; b 2
Y 32
X 2
m –13
13
; b 1
Y 13
X 1
m 34
; b 0
Y 34
X
m 24
12
;b 1
Y 12
X 1
7 3 4 9 ÷3
4 16 9 ÷27
64 9 ÷27
55÷27 2 127
4 2 8 7 5 19
6 64 35 19
6 64 35 19 54
13 5÷10 169 5÷10
169 .5 169.5
5 9 2 6 7 2 3 5 7 6 7 8 3
35 42 24 17
2X 5 X 132X X 13 5
3X 18X 6
Y 14 3Y 0Y 3Y 14
2Y 14Y 7
3 12
B 23
5 14
56
B
12 72
B 23
12 214
56
B
42B 8 63 10B8 63 10B 42B
55 52B5552
B
B 5552
or –1 352
2.7T 1.09 5.3 .6T
100 2.7T 1.09 100 5.3 .6T
270T 109 530 60T270T 60T 530 109
330T 421
T 421330
or 1 91330
2 3
2
2
3
[ ]
[ ]
[ ] [ ]
( )
( )
( ) ( ) ( ) ( )
−
= = = −
= −
= = − =
= − +
= =
=
= = = −
= −
− × − =× − =
− =
=
− − + − × + =− + − + =
+ − + =
+ = += + =
− − + ⋅ = − + ⋅= − + =
− = − ++ = +
==
+ − =− = −− = −
=
− + = +
− +
= +
− + = +− = +− =
− =
= −
+ = −+ = −+ = −+ = −
=
=
Systematic Review 7D1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
4
3
m 35
; b 4
Y 35
X 4
m 46
23
; b 0
Y 23
X
m 36
12
; b 1
Y 12
X 1
m 63
2; b 3
Y 2X 3
5 8 4 7 12
3 4 7 12
3 4 7 12
12 7 12 7
7 2 48 5
49 2 48 5
98 48 5 141
144 ÷9 3 100 121
144 ÷9 3 21
144 ÷9 3 21
16 3 21 27
8 17 3 2 6 5
8 17 6 36 25
8 11 36 25
88 36 25 99
4A 11 A 44A A 4 11
3A 15A 5
5F 6F 85F 6F
F 8
25
16
D 34
60 25
16
D 60 34
24 10D 4510D 45 2410D 69
D 6910
or 6 910
.03M 1.2 .48M
100 .03M 1.2 100 .48M
3M 120 48M3M 48M 120
51M 120
M 12051
or 2 617
= =
= +
=−
= − =
= −
=−
= − =
= − +
= = =
= +
− − × − + =− − × − + =− × − + =
− − + = −
− × − + =− × − + =
− − + = −
× − − =× − − =× − =× − =
− × + − − =− + − =
+ − =+ − =
+ = −− = − −
= −= −
− = − +− + =
=
− = −
−
= −
− = −− = − −− = −
=
− = −− = −− = −+ =
=
=
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
4
3
m 35
; b 4
Y 35
X 4
m 46
23
; b 0
Y 23
X
m 36
12
; b 1
Y 12
X 1
m 63
2; b 3
Y 2X 3
5 8 4 7 12
3 4 7 12
3 4 7 12
12 7 12 7
7 2 48 5
49 2 48 5
98 48 5 141
144 ÷9 3 100 121
144 ÷9 3 21
144 ÷9 3 21
16 3 21 27
8 17 3 2 6 5
8 17 6 36 25
8 11 36 25
88 36 25 99
4A 11 A 44A A 4 11
3A 15A 5
5F 6F 85F 6F
F 8
25
16
D 34
60 25
16
D 60 34
24 10D 4510D 45 2410D 69
D 6910
or 6 910
.03M 1.2 .48M
100 .03M 1.2 100 .48M
3M 120 48M3M 48M 120
51M 120
M 12051
or 2 617
2
2 2[ ][ ]
[ ] [ ]
( )
( )
( )( )
( )
( )
( )
= =
= +
=−
= − =
= −
=−
= − =
= − +
= = =
= +
− − × − + =− − × − + =− × − + =
− − + = −
− × − + =− × − + =
− − + = −
× − − =× − − =× − =× − =
− × + − − =− + − =
+ − =+ − =
+ = −− = − −
= −= −
− = − +− + =
=
− = −
−
= −
− = −− = − −− = −
=
− = −− = −− = −+ =
=
=
11.-5 -4 -3 -2 -1 0 1 2 3 4 5
12.-5 -4 -3 -2 -1 0 1 2 3 4 5
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
4
3
m 35
; b 4
Y 35
X 4
m 46
23
; b 0
Y 23
X
m 36
12
; b 1
Y 12
X 1
m 63
2; b 3
Y 2X 3
5 8 4 7 12
3 4 7 12
3 4 7 12
12 7 12 7
7 2 48 5
49 2 48 5
98 48 5 141
144 ÷9 3 100 121
144 ÷9 3 21
144 ÷9 3 21
16 3 21 27
8 17 3 2 6 5
8 17 6 36 25
8 11 36 25
88 36 25 99
4A 11 A 44A A 4 11
3A 15A 5
5F 6F 85F 6F
F 8
25
16
D 34
60 25
16
D 60 34
24 10D 4510D 45 2410D 69
D 6910
or 6 910
.03M 1.2 .48M
100 .03M 1.2 100 .48M
3M 120 48M3M 48M 120
51M 120
M 12051
or 2 617
2
2 2[ ][ ]
[ ] [ ]
( )
( )
( )( )
( )
( )
( )
= =
= +
=−
= − =
= −
=−
= − =
= − +
= = =
= +
− − × − + =− − × − + =− × − + =
− − + = −
− × − + =− × − + =
− − + = −
× − − =× − − =× − =× − =
− × + − − =− + − =
+ − =+ − =
+ = −− = − −
= −= −
− = − +− + =
=
− = −
−
= −
− = −− = − −− = −
=
− = −− = −− = −+ =
=
=
aLGeBra 1
sYsteMatic reVieW 7D - Lesson Practice 8a
soLutions180
20.
4
3
m 35
; b 4
Y 35
X 4
m 46
23
; b 0
Y 23
X
m 36
12
; b 1
Y 12
X 1
m 63
2; b 3
Y 2X 3
5 8 4 7 12
3 4 7 12
3 4 7 12
12 7 12 7
7 2 48 5
49 2 48 5
98 48 5 141
144 ÷9 3 100 121
144 ÷9 3 21
144 ÷9 3 21
16 3 21 27
8 17 3 2 6 5
8 17 6 36 25
8 11 36 25
88 36 25 99
4A 11 A 44A A 4 11
3A 15A 5
5F 6F 85F 6F
F 8
25
16
D 34
60 25
16
D 60 34
24 10D 4510D 45 2410D 69
D 6910
or 6 910
.03M 1.2 .48M
100 .03M 1.2 100 .48M
3M 120 48M3M 48M 120
51M 120
M 12051
or 2 617
[ ] [ ]
= =
= +
=−
= − =
= −
=−
= − =
= − +
= = =
= +
− − × − + =− − × − + =− × − + =
− − + = −
− × − + =− × − + =
− − + = −
× − − =× − − =× − =× − =
− × + − − =− + − =
+ − =+ − =
+ = −− = − −
= −= −
− = − +− + =
=
− = −
−
= −
− = −− = − −− = −
=
− = −− = −− = −+ =
=
=
Systematic Review 7E1.
2.
3.
4.
5.
up
slope
m b
Y X
m
=−
= − =
= − +
=−
= −
25
25
2
25
2
28
1
;
443
14
3
33
1 1
1
31
;
;
b
Y X
m b
Y X
m
=
= − +
= = = −
= −
=−
= −
6.
7.
8.
9. 33 2
3 2
11 3 14 2
11 9 14
2
; b
Y X
= −
= − −
⋅ − × =⋅( ) −
10.
11.
12.
13.
××( ) =( ) − ( ) =
⋅ + − =⋅( ) + − =
+
2
99 28 71
2 7 4 15
2 7 16 1514 1
214.
66 15 15
6 8 3
36 8 9
36 1 35
1
2 2
− =
−( ) + −( ) =+ −( ) =
+ −( ) =
15.
16. 66 8 5 142 5 1410 14 4
2 5 3 4 1 10
÷ ⋅ − =⋅ − =
− = −
− + − + = − + −17. B B B B−− + + − = − + −
− + = − −− + = − −
= −
2 5 3 4 1 102 3 9
3 9 22 11
B B B BB B
B BB
B == − = −
+ − − = − + + −− + − = − +
112
5 12
5 6 9 2 6 3 35 6 9 2 3
18. K K K KK K K KK
K KK K
KK
G
+ −− = +− = +
==
= − +
6 34 3 34 3 3
3 62
4 310
23
89
90 4
19.
1.
2.
3.
4.
5.
up
slope
m b
Y X
m
=−
= − =
= − +
=−
= −
25
25
2
25
2
28
1
;
443
14
3
33
1 1
1
31
;
;
b
Y X
m b
Y X
m
=
= − +
= = = −
= −
=−
= −
6.
7.
8.
9. 33 2
3 2
11 3 14 2
11 9 14
2
; b
Y X
= −
= − −
⋅ − × =⋅( ) −
10.
11.
12.
13.
××( ) =( ) − ( ) =
⋅ + − =⋅( ) + − =
+
2
99 28 71
2 7 4 15
2 7 16 1514 1
214.
66 15 15
6 8 3
36 8 9
36 1 35
1
2 2
− =
−( ) + −( ) =+ −( ) =
+ −( ) =
15.
16. 66 8 5 142 5 1410 14 4
2 5 3 4 1 10
÷ ⋅ − =⋅ − =
− = −
− + − + = − + −17. B B B B−− + + − = − + −
− + = − −− + = − −
= −
2 5 3 4 1 102 3 9
3 9 22 11
B B B BB B
B BB
B == − = −
+ − − = − + + −− + − = − +
112
5 12
5 6 9 2 6 3 35 6 9 2 3
18. K K K KK K K KK
K KK K
KK
G
+ −− = +− = +
==
= − +
6 34 3 34 3 3
3 62
4 310
23
89
90 4
11.-5 -4 -3 -2 -1 0 1 2 3 4 5
12.-5 -4 -3 -2 -1 0 1 2 3 4 5
1.
2.
3.
4.
5.
up
slope
m b
Y X
m
=−
= − =
= − +
=−
= −
25
25
2
25
2
28
1
;
443
14
3
33
1 1
1
31
;
;
b
Y X
m b
Y X
m
=
= − +
= = = −
= −
=−
= −
6.
7.
8.
9. 33 2
3 2
11 3 14 2
11 9 14
2
; b
Y X
= −
= − −
⋅ − × =⋅( ) −
10.
11.
12.
13.
××( ) =( ) − ( ) =
⋅ + − =⋅( ) + − =
+
2
99 28 71
2 7 4 15
2 7 16 1514 1
214.
66 15 15
6 8 3
36 8 9
36 1 35
1
2 2
− =
−( ) + −( ) =+ −( ) =
+ −( ) =
15.
16. 66 8 5 142 5 1410 14 4
2 5 3 4 1 10
÷ ⋅ − =⋅ − =
− = −
− + − + = − + −17. B B B B−− + + − = − + −
− + = − −− + = − −
= −
2 5 3 4 1 102 3 9
3 9 22 11
B B B BB B
B BB
B == − = −
+ − − = − + + −− + − = − +
112
5 12
5 6 9 2 6 3 35 6 9 2 3
18. K K K KK K K KK
K KK K
KK
G
+ −− = +− = +
==
= − +
6 34 3 34 3 3
3 62
4 310
23
89
90 4
66 15 15
6 8 3
36 8 9
36 1 35
1
2 2
− =
−( ) + −( ) =+ −( ) =
+ −( ) =
15.
16. 66 8 5 142 5 1410 14 4
2 5 3 4 1 10
÷ ⋅ − =⋅ − =
− = −
− + − + = − + −17. B B B B−− + + − = − + −
− + = − −− + = − −
= −
2 5 3 4 1 102 3 9
3 9 22 11
B B B BB B
B BB
B == − = −
+ − − = − + + −− + − = − +
112
5 12
5 6 9 2 6 3 35 6 9 2 3
18. K K K KK K K KK
K KK K
KK
G
+ −− = +− = +
==
= − +
6 34 3 34 3 3
3 62
4 310
23
89
90 4
19.
3310
90 23
89
387 60 80447 80447
= − +
= − +=
G
GG
88044780
5 4780
5 6 9 8
10 5 6 10 9
=
= =
− − = −− −( ) = −
G
G
R
R
20. . .
. ..8
50 6 986 98 506 48
8
( )− − = −
− = − +− = −
=
RRRR
Lesson Practice 8A1. Y X m b= − = = −1
42 1
42, ,
Y
X
aLGeBra 1
Lesson Practice 8a - Lesson Practice 8B
soLutions 181
2. Y X m b= − + = − =2 1 2, ,
Y
X
3. Y m b= − = = −2 0 2; ,Y
X
4. Y X m b= + = =35
1 35
1, ,
Y
X
5. Y Y X m b= = + = =X; , ,0 1 0
Y
X
6. X= − ==
3, ,m undefined
b none or undefined
Y
X
Lesson Practice 8B1. Y X m b= − − = − = −2 5 2 5, ,
Y
X
aLGeBra 1
Lesson Practice 8B - sYsteMatic reVieW 8c
soLutions182
2. Y X Y X m b= − = − + = − =32
32
0 32
0; , ,
Y
X
3. X m undefined
b none or undefined
graph i
= ==
0, ,
;
ss Y axis
X
-
= 0X = 0 Y
X
4. Y X m b= − + = − =3 2 3 2, ,
Y
X
5. Y X m b= − = = −2 1 2 1, ,
Y
X
6. Y Y X m b= = + = =4 0 4 0 4; , ,
Y
X
Systematic Review 8C 1. days dollars
0 4
1 5
2 6
3 7
−−−−
2. see graph
dollars
days
#2
#5
line g: #10
aLGeBra 1
sYsteMatic reVieW 8c - sYsteMatic reVieW 8D
soLutions 183
3.
4.
5.
− = − −
−−−
1 4 4
0 2
0 0
1 2
2 4
3 6
; ; $
;
D
days money
see ggraph
intercept
6.
7.
8.
9.
−= =
= +
2 0
4 2
4 2
;
;slope
Y X
quaadrants
R RR
, ,1 2 3
60 90 7030 7
10.
11.
see graph
− =− = 00
2 13
18 54 27
9 2 6 9 3
2 6 36 5
R
X
X
XX
X
= −
− + =− +( ) = ( )− + =
=
=
12.
556
6 5 1 12 3 2
11 1 12 3 2
121
2
2
13. +( ) −
= + −
−( ) = +
÷
÷
X X
X X
−−( ) ====
− = −
1 12 5120 12 5
10 52
4 32 36 8
4
÷÷
XXX
X
B B B BY
B
14.
11 8 4 9 2
7 9 216 2
8
100 1 03 10
−( ) = −( )− = −
− = −=
( ) −
B Y
YY
Y
15. . 00 8 100 5
103 80 50080 397
39780
4 77
. Y
YY
Y
Y
( ) = ( )− =− =
=−
= −880
60 154
60 115
60 236
225 132 2
15 12 1016. ( ) = ( ) + ( )= +
Y
Y 330225 362
362225
1137225
5 20 50 3555
Y
Y
Y
X X
=
=
=
− = +− =
17.445
5545
1 29
60 310
60 196
60
X
X
X
X X
= −
= −
11 8 4 9 2
7 9 216 2
8
100 1 03 10( ) −15. . 00 8 100 5
103 80 50080 397
39780
4 77
. Y
YY
Y
Y
( ) = ( )− =− =
=−
= −880
60 154
60 115
60 236
225 132 2
15 12 1016. ( ) = ( ) + ( )= +
Y
Y 330225 362
362225
1137225
5 20 50 3555
Y
Y
Y
X X
=
=
=
− = +− =
17.445
5545
1 29
60 310
60 196
606 10 15
X
X
X
X X
= −
= −
( ) − ( ) = ( )18. 1174
18 190 255172 255
255172
1 83172
X XX
X
X
− =− =
=−
= −
19. WWF WF WF
WF WF WF
× = × = =
× = × = =
7 57
7 57
57
5 25
5 25
25
; ;
; ;20.
Systematic Review 8D1.
2.
3.
days dollars
0 3
1 5
2 7
3 9
2 3
−−−−
− =see graph
; ; $ −− −2 3
2 3
0 2
1 5
2 8
3 11
D
days dollars
4.
5.
;
line g is the X-axis: see graph
slope intercept
6.
7.
3 2
1
;
;= − = 00
8.
9.
10.
Y X
se
= −quadrants 2; 4
e graph
aLGeBra 1
sYsteMatic reVieW 8D - sYsteMatic reVieW 8e
soLutions184
2 3
2 3
0 2
1 5
2 8
3 11
D
days dollars
4.
5.
;
line g is the X-axis: see graph
slope intercept
6.
7.
3 2
1
;
;= − = 00
8.
9.
10.
Y X
se
= −quadrants 2; 4
e graph
dollars
days
F
#5#2
line g: #10
11.
12.
12 6 2412 18
1812
1 12
72 60 4860
YY
Y
Y
FF
= −= −
= −
= −
− + ====
− +( ) − + −( ) =
−( )
1202
2 5 4 2 3 3 8 9 4 0
4 5 7 2
2
F
X X X
X
13.
−− +( ) =− − −[ ] =
−( ) =−
3 8 5 0
4 35 10 24 15 0
4 11 25 0
44
X
X X
X
1100 044 100
441001125
50 30 80 40
XX
X
X
BY B BY
==
=
=
− + = −14. BB
B Y B Y
Y YY
Y
10 5 3 10 8 4
5 3 8 47 13
713
10
− +( ) = −( )− + = −
=
=
15. 000 018 1000 25 1000 2 04
18 250 2040
202
. . .( ) = ( )+ ( )= +
−
Q
Q
22 250
2022250
8 11125
24 138
24 133 8
=− =
= −
( ) − + ( )
Q
Q
Q
M16.33
24 76
39 104 2876 397639
13739
10 1
4= ( )− + =
=
=
=
−
MM
M
M
1125
50 30 80 40
XX
X
X
BY B BY
==
=
=
− + = −14. BB
B Y B Y
Y YY
Y
10 5 3 10 8 4
5 3 8 47 13
713
10
− +( ) = −( )− + = −
=
=
15. 000 018 1000 25 1000 2 04
18 250 2040
202
. . .( ) = ( )+ ( )= +
−
Q
Q
22 250
2022250
8 11125
24 138
24 133 8
=− =
= −
( ) − + ( )
Q
Q
Q
M16.33
24 76
39 104 2876 397639
13739
10 1
4= ( )− + =
=
=
=
−
MM
M
M
17. .. . .3 10 2 6 10 5 2
13 26 5213 52
14
36
( ) + ( ) = ( )− + =
=
=
X
XX
X
18. 00 75
30 256
30 73
42 125 7042 55
5542
5 10( ) = ( ) − ( )= −=
=
Y
YY
Y
YY
N N N
WF WF WF
=
− + +
× = × = =
11342
3 2 7
4 34
4 34
34
19.
20. ; ;
Systematic Review 8E1.
2.
3.
days dollars
D
0 4
1 1
2 2
3 5
3 4 3
−−
= −see graph
; ; $ 44 3 4
3 1
0 3
1 2
2 1
3 0
;
or M D
days dollars
= −−
−−−
4.
5. see ggraph
y-intercept
6.
7.
8.
1 3
3 2
3 2
;
;
−= − =
= − +slope
Y X
99.
10.
quadrants 1, 2, 4
see graph
aLGeBra 1
sYsteMatic reVieW 8e - Lesson Practice 9a
soLutions 185
1.
2.
3.
days dollars
D
0 4
1 1
2 2
3 5
3 4 3
−−
= −see graph
; ; $ 44 3 4
3 1
0 3
1 2
2 1
3 0
;
or M D
days dollars
= −−
−−−
4.
5. see ggraph
y-intercept
6.
7.
8.
1 3
3 2
3 2
;
;
−= − =
= − +slope
Y X
99.
10.
quadrants 1, 2, 4
see graph
Y
X
line g: #10
#5
#2
11. − − + =− − +( ) = ( )− − + =
− = −
9 24 15 0
3 3 8 5 3 0
3 8 5 0
11
Q Q
Q Q
Q Q
Q 55
511
66 99 77 0
11 6 9 7 11 0
6 9 7 09
Q
A
A
AA
=
+ − =+ −( ) = ( )+ − =
12.
−− ==
=
− + − −( ) − = −( )−( ) − =
1 09 1
19
2 3 7 4 8 1 4 4
2 9 16
2
A
A
X
X
13.
−−( )− =
= −
+ = −= −= −
4
18 1223
12 28 2040 20
2
10 4
X
X
BB
B
14.
15. DD D
D DDD
( ) − ( ) = ( )− =
==
10 3 10 18 5
40 3 18537 185
5
735
. .
16. 00 132
70 57
70 135
455 50 182455 13
10 14( ) = ( ) − ( )= −= −
N N
N N22
455132
3 59132
12 2 66 2
3
N
N
N
AA
A
−( ) − =
1 09 1
19
2 3 7 4 8 1 4 4
2 9 16
A
A
X
X −−( )− =
= −
+ = −= −= −
4
18 1223
12 28 2040 20
2
10 4
X
X
BB
B
14.
15. DD D
D DDD
( ) − ( ) = ( )− =
==
10 3 10 18 5
40 3 18537 185
5
735
. .
16. 00 132
70 57
70 135
455 50 182455 13
10 14( ) = ( ) − ( )= −= −
N N
N N22
455132
3 59132
12 2 66 2
3
20
N
N
N
AA
A
−=
= −
− = − −− = −
=
17.
18. 440 112
40 198
40 910
220 95 36220 5
5 4( ) − + ( ) = ( )− + =
− = −
X
XX 99
59220
1 4
9 79
9 79
7
X
N N
WF WF WF
=
+( ) −( )
× = × = =
19.
20. ; ;99
Lesson Practice 9ALessonPractice 8A.11. a m b Y X
b m
. , ,
.
= = = +53
5 53
5
== = = +
= = − = −
=
53
1 53
1
53
1 53
1
53
, ,
. , ,
.
b Y X
c m b Y X
d m ,, ,
. , ,
.
b Y X
w m b Y X
x m
= − = −
= − = = − +
= −
4 53
4
12
4 12
42.
112
2 12
2
12
1 12
1
, ,
. , ,
.
b Y X
y m b Y X
z m
= = − +
= − = − = − −
= −− = − = − −
= −
= −= −
12
3 12
3
13
2
3
4
, ,
.
.
.
b Y X
A Y X
B Y X
C Y
3.
33 3 4
3
X Y X
Lines B C both have a slope of
w
;
& ,
= − +−
hhich is the same as Y X
Answers B C are pa
.
&
= − +3 2
rrallel to the given line.
4. A. Y 14
X 5
B. Y 12
= +
= − XX 2
C. Y 4 48
X; Y 12
X 4
+
= + = +
aLGeBra 1
Lesson Practice 9a - Lesson Practice 9a
soLutions186
53
1 53
1
53
1 53
1
53
, ,
. , ,
.
b Y X
c m b Y X
d m ,, ,
. , ,
.
b Y X
w m b Y X
x m
= − = −
= − = = − +
= −
4 53
4
12
4 12
42.
112
2 12
2
12
1 12
1
, ,
. , ,
.
b Y X
y m b Y X
z m
= = − +
= − = − = − −
= −− = − = − −
= −
= −= −
12
3 12
3
13
2
3
4
, ,
.
.
.
b Y X
A Y X
B Y X
C Y
3.
33 3 4
3
X Y X
Lines B C both have a slope of
w
;
& ,
= − +−
hhich is the same as Y X
Answers B C are pa
.
&
= − +3 2
rrallel to the given line.
4. A. Y 14
X 5
B. Y 12
= +
= − XX 2
C. Y 4 48
X; Y 12
X 4
+
= + = +
Line C has a reduced sllope of
which is the same slope as Y X
,1212
5= − ..
.Answer C is parallel to the given line
5. A. Y ==
= =
= − = − +
23
32
X + 4
B. Y 64
X; Y X
C. 2Y 8 3X; 2Y 3X 8,
YY 32
X 4
Given line: 2Y 3X 4;
2Y 3X 4; Y 32
X 2
= − +
− =
= + = +
LIne B has a reduced slope of 32
,
which is thhe same slope as Y 3 X 2.
A. Y 129
X 1; Y 43
= +
= − =
2
6. XX 1
B. 3Y 4X 0; Y 43
X
C. 2Y 5X 8; Y 52
X 4
−
= − + = −
− = − = − +
Giiven line Y X Y X
Y X
Line B
: ; ;3 4 6 3 4 6
43
2
+ = − = − −
= − −
hhas a slope of
which is the same slope as
,− 43
.Y X
Answer B is parallel to the given li
= − −43
2
nne.
7.
8.
9.
− + =− = − +
= −
− == +=
− −
Y XY xY X
Y XY XY X
Y
2 42 4
2 4
4 04 04
2 XXY X
Y X
Y XY X
Y X
= −− = −
= − +
− = −= −
= −
22 2
12
1
3 2 63 2 6
23
2
10.
11..
12.
7.
8.
9.
− + =− = − +
= −
− == +=
− −
Y XY xY X
Y XY XY X
Y
2 42 4
2 4
4 04 04
2 XXY X
Y X
Y XY X
Y X
= −− = −
= − +
− = −= −
= −
22 2
12
1
3 2 63 2 6
23
2
10.
11..
12.
− − = −− = −
= − +
= − −
+ = −
4 38
34
2
53
2
53
Y X
Y X
Y X
X Y
84Y 3X
22 53
5 3 6
.Adding X to both ides
X Y Multiplyin
s
+ = − gg each term by
Y XX Y
or X Y M
.3
4 34 3
4 3
13. = −− + = −
− = uultiplying each term by
Y X
X Y
.−
= +
− + =
1
14
3
14
3
14.
−− + = − −
= − −
+ = −
+
X Y or
Y X
X Y
X Y
4 12
35
1
35
1
3 5
X 4Y = 12
15.
== −
=− + = − =
5
33 0 3 0
16. Y XX Y or X Y
aLGeBra 1
Lesson Practice 9B - Lesson Practice 9B
soLutions 187
Lesson Practice 9B1. Y X Y X= − = −6
83 3
43;
Y
X
2. Y X Y X= + = +33
4 4;
Y
X
3. slope-intercept:
standard form:
;Y X Y
Y
= − = −0 2 2
== −2
Y
X
4. slope-intercept: Y X 2;
Y X 2
standard
= − +
= − +
86
43
fform: ;43
2
4 3 6
X Y
X Y
+ =
+ =Y
X
5. slope ercept
X
s dard f
− = −
= −
int :
tan
Y X + 0;
Y
63
2
oorm X Y: 2 0+ =Y
X
6. slope-intercept: none because
slope is undefinned and there is
no Y-intercept. standard form:: X = 3
Y
X
aLGeBra 1
Lesson Practice 9B - sYsteMatic reVieW 9c
soLutions188
7.
8.
see graph
slope = − 32
Y
X
2
-3
#7#12
9.
10.
11.
12.
y-intercept
:
see gr
=
= − +
= −
3
32
3
32
Y X
C Y X
aaph on previous page
13.
14.
Y X
Y X X
= − −
+ = −
32
2
32
2 3; ++ = −
= =
2 4
82
4
Y
slope
15.
16.
17.
see graph below
y-interrcept
see graph below
= −= −
=
1
4 1
4
18.
19.
20.
21.
Y X
C
Y X ++− = − − + =
3
4 3 4 322. X Y or X Y
It is customary to writee the standard form
of the equation of a line suuch that
the X coefficient is positive, but eitther form
is correct.
9.
10.
11.
12.
y-intercept
:
see gr
=
= − +
= −
3
32
3
32
Y X
C Y X
aaph on previous page
13.
14.
Y X
Y X X
= − −
+ = −
32
2
32
2 3; ++ = −
= =
2 4
82
4
Y
slope
15.
16.
17.
see graph below
y-interrcept
see graph below
= −= −
=
1
4 1
4
18.
19.
20.
21.
Y X
C
Y X ++− = − − + =
3
4 3 4 322. X Y or X Y
It is customary to writee the standard form
of the equation of a line suuch that
the X coefficient is positive, but eitther form
is correct.
Y
X
2
8
#15
#20
Systematic Review 9C 1.
2.
3.
4.
see graph
y-intercept
slope
Y X
X
= =
== +−
33
1
4
4
YY or X Y
A Y X
C Y X
= − − + == − −= −
4 4
15.
6.
:
:
see graph
Y
X
3
3
#3 #6
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
2
Y 3X 1, so slope is 3
Y 13
X 2
X 3Y 6 or X 3Y 6
2Y 3X 1; Y 32
X 12
3 11 2÷16 7 3Y 4Y 9
8 2÷16 7 Y 9
64 2÷16 7 Y 9128 ÷16 Y 16
8 Y 168 YY 8
3 5 6 4 X 3X
2 2 X 3X
4 2 4X6 4X64
X
X 1 12
3 A 4 5 2A 6 21
3A 12 10A 30 217A 18 21
7A 3
A 37
15 43
15 45
A 15 115
20 12A 3312A 13
A 1312
A 1 112
6 6
6 6 6 6
36 36 72
5 5 7 10 7 17
7 7 7
8 8 8 64
25% .25
.25 76.98 $19.25
45% .45
.45 600 270 people
2
2
2
2
5 3 3
2 2
2
( ) ( ) ( )
( )( )
( )
( )
( )( ) ( ) ( )
( ) ( ) ( )
( )
( )
( ) ( )( )
= − − −
− =
− = − − + =
= − + = − +
− × − = − +
− × − = − +× − = − +
= − += − +
− = −=
− + − − =
− + − =+ =
=
=
=
− − − =− − + =
− + =− =
= −
+ =
+ ==
=
=
− − − =− × − − − =
− − = −+ − − = + + =
− − − = − = −
− = − − ==
× ==
× =
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
2
Y 3X 1, so slope is 3
Y 13
X 2
X 3Y 6 or X 3Y 6
2Y 3X 1; Y 32
X 12
3 11 2÷16 7 3Y 4Y 9
8 2÷16 7 Y 9
64 2÷16 7 Y 9128 ÷16 Y 16
8 Y 168 YY 8
3 5 6 4 X 3X
2 2 X 3X
4 2 4X6 4X64
X
X 1 12
3 A 4 5 2A 6 21
3A 12 10A 30 217A 18 21
7A 3
A 37
15 43
15 45
A 15 115
20 12A 3312A 13
A 1312
A 1 112
6 6
6 6 6 6
36 36 72
5 5 7 10 7 17
7 7 7
8 8 8 64
25% .25
.25 76.98 $19.25
45% .45
.45 600 270 people
2
2
2
2
5 3 3
2 2
2
( ) ( ) ( )
( )( )
( )
( )
( )( ) ( ) ( )
( ) ( ) ( )
( )
( )
( ) ( )( )
= − − −
− =
− = − − + =
= − + = − +
− × − = − +
− × − = − +× − = − +
= − += − +
− = −=
− + − − =
− + − =+ =
=
=
=
− − − =− − + =
− + =− =
= −
+ =
+ ==
=
=
− − − =− × − − − =
− − = −+ − − = + + =
− − − = − = −
− = − − ==
× ==
× =
aLGeBra 1
sYsteMatic reVieW 9c - sYsteMatic reVieW 9D
soLutions 189
13.
14.
15.
16.
17.
18.
19.
20.
2
Y 3X 1, so slope is 3
Y 13
X 2
X 3Y 6 or X 3Y 6
2Y 3X 1; Y 32
X 12
3 11 2÷16 7 3Y 4Y 9
8 2÷16 7 Y 9
64 2÷16 7 Y 9128 ÷16 Y 16
8 Y 168 YY 8
3 5 6 4 X 3X
2 2 X 3X
4 2 4X6 4X64
X
X 1 12
3 A 4 5 2A 6 21
3A 12 10A 30 217A 18 21
7A 3
A 37
15 43
15 45
A 15 115
20 12A 3312A 13
A 1312
A 1 112
6 6
6 6 6 6
36 36 72
5 5 7 10 7 17
7 7 7
8 8 8 64
25% .25
.25 76.98 $19.25
45% .45
.45 600 270 people
5 3 3
2 2
2
( ) ( ) ( )
[ ]
( )( )
( )
( )
( )( ) ( ) ( )
( ) ( ) ( )
( )
( )
( ) ( )( )
= − − −
− =
− = − − + =
= − + = − +
− × − = − +
− × − = − +× − = − +
= − += − +
− = −=
− + − − =
− + − =+ =
=
=
=
− − − =− − + =
− + =− =
= −
+ =
+ ==
=
=
− − − =− × − − − =
− − = −+ − − = + + =
− − − = − = −
− = − − ==
× ==
× =
Systematic Review 9D1.
2.
3.
4.
see graph
y-intercept
slope
Y X
X
= =
= −= −
66
1
4
4
−− = − + = −
= +
Y or X Y
C Y X
4 4
14
2:5.
6. see graph
Y
X
6
6
#3
#6
7.
8.
9.
Y X
Y X slope
X Y or X Y
= −
= − + = −− = − − + =
14
1
2 3 2
2 5 2
;
55
4 2 8 12
2
1 1 1 1 1 12 2
10.
11.
Y X Y X
B
= − + = − +
− − − − = −( ) + −( )
;
÷÷
÷
1
4 1 1
4 116 1
1515
3 5 8
2
2
2
− = −
= −− = −
= −= −
+( ) + −
B
BBB
B
12. 111 4 2
8 3 4 8
64 3 8 375 3
25
5
2
+ = −( )+ − + = −+ + =
==
Z Z
Z Z
ZZ
Z
B13. −−( ) + +( ) =− + + =
− ==
6 4 2 7 102
5 30 8 28 10213 2 102
13 10
B
B BB
B 448
55 30 125
25 125
5
8
B
Q Q
Q
Q
=
− ===
− − − −( ) { } = −
14.
15. −−[ ]{ } =
− = − ×( ) = −− −( ) =
+ −( )
8 8
9 9 9 81
4 4
3 3
2
2 2
16.
17.
18. == + ==× =
× =
= =
9 9 18
76 76
76 200 152
88 2
8
28
19.
20.
% .
. $
WF
WF 114
14
81
22
check: × =
7.
8.
9.
Y X
Y X slope
X Y or X Y
= −
= − + = −− = − − + =
14
1
2 3 2
2 5 2
;
55
4 2 8 12
2
1 1 1 1 1 12 2
10.
11.
Y X Y X
B
= − + = − +
− − − − = −( ) + −( )
;
÷÷
÷
1
4 1 1
4 116 1
1515
3 5 8
2
2
2
− = −
= −− = −
= −= −
+( ) + −
B
BBB
B
12. 111 4 2
8 3 4 8
64 3 8 375 3
25
5
2
+ = −( )+ − + = −+ + =
==
Z Z
Z Z
ZZ
Z
B13. −−( ) + +( ) =− + + =
− ==
6 4 2 7 102
5 30 8 28 10213 2 102
13 10
B
B BB
B 448
55 30 125
25 125
5
8
B
Q Q
Q
Q
=
− ===
− − − −( ) { } = −
14.
15. −−[ ]{ } =
− = − ×( ) = −− −( ) =
+ −( )
8 8
9 9 9 81
4 4
3 3
2
2 2
16.
17.
18. == + ==× =
× =
= =
9 9 18
76 76
76 200 152
88 2
8
28
19.
20.
% .
. $
WF
WF 114
14
81
22
check: × =
aLGeBra 1
sYsteMatic reVieW 9e - Lesson Practice 10a
soLutions190
Systematic Review 9E1.
2.
3.
4.
see graph
y-intercept
slope
Y
=−
= −
= −= −
42
2
3
2XX X Y
B Y X C
− + = −=
3 2 3
3
;
: ;5.
6. see graph
line will hhave a slope of 3( )
Y
X
4
-2
#3 #6
7.
8.
9.
10.
11.
Y X
X Y
Y X Y X
Y
= −−
+ = −+ = − = − −
3 2
15
3 6
2 1 2 1
24
;
−− + = −− + − = −
=
=
− − −
108 96 48 1284 96 48 12
48 7223
Y YY Y
Y
Y
12. 99 7 5 2 4
9 49 5 2 4
40 5 2 4
8
2( ) +{ } = +
− +{ } = += +
÷ ÷
÷ ÷
÷ ÷
Q
Q
Q
÷÷2 4
4 4
0
8 3 9 4 2 5 2 4
8 24 72
= += +=
+ −( ) − +( ) = ++ −
Q
Q
Q
A A A
A
13.
−− − = +− − = +
− = +− =
= −
8 20 2 424 72 20 2 4
68 2 472 2
36
A AAAA
A
14. 66 6 100 1 14 5 9
12 99 196 45
144 99 19
2 2
2
+( ) + − − = × +
+ − = ++ −
B
B
66 452
6 9 3 5 5 5
5
− ==
− − − + −( ) = − − −( ) = −
−
BB
15.
16. 33 5 5 5 125
1010 3
10
310
101
3
= − × ×( ) = −
× =
× =
17.
1
WF
check:
88.
19.
20.
8 75 25 35
6 06 06 115 6 90
. .
% . ; . $ .
÷ == × =
packs
−− − = +− − = +
− = +− =
= −
8 20 2 424 72 20 2 4
68 2 472 2
36
A AAAA
A
14. 66 6 100 1 14 5 9
12 99 196 45
144 99 19
2 2
2
+( ) + − − = × +
+ − = ++ −
B
B
66 452
6 9 3 5 5 5
5
− ==
− − − + −( ) = − − −( ) = −
−
BB
15.
16. 33 5 5 5 125
1010 3
10
310
101
3
= − × ×( ) = −
× =
× =
17.
1
WF
check:
88.
19.
20.
8 75 25 35
6 06 06 115 6 90
. .
% . ; . $ .
÷ == × =
packs
−− −N N2 2
Lesson Practice 10A1.
2.
3.
4.
5.
see graph
y-intercept
slope
Y X
B
= =
==
82
4
0
4
::
see graph
Y X= − 14
6.
Y
X8
#6
#3
2
7.
8.
9.
10.
Y X
Y X
X Y
slope
= − +
+ =
+ =
14
2
14
2
4 8
on the graph
== − = −
= −= − −
= −
22
1
2
2
2
11.
12.
13.
14
y-intercept
:
Y X
A Y X
..
15.
16.
on the graph
Y X
X Y or X Y
= +− = − − + =
2
2 2
aLGeBra 1
Lesson Practice 10a - sYsteMatic reVieW 10c
soLutions 191
Y
X2
#11
#14
-2
Lesson Practice 10B1.
2.
3.
4.
se
slope
Y
e graph
y-intercept
= − = −
=
= −
28
14
2
144
2
4 5
X
A Y X
+
= −5.
6.
:
see graph
Y
X
-2
#6
#3
8
7.
8.
9.
Y X
X Y or X Y
= +− = − − + =4 4
4 4 4 4
see graph
Y
X
#14
#11
4
4
10.
11.
12.
13.
slope
Y X
A Y X
= =
== +
= −
44
1
1
1
y-intercept
: ++
= − −+ = −
1
4
4
14.
15.
16.
see graph
Y X
X Y
Systematic Review 10C1. see graph
Systematic Review 9C 1. on the graph
2.
3.
4.
5. B, C: Y = −3X − 1
6. on the graph
7. Y = −3X + 6
3X + Y = 6
8. on the graph
9. Y = -3X − 4
3X + Y = −4
10. slopes are the same, so lines are parallel
11. 6X − X + 3 = 4X + 7
5X + 3 = 4X + 7
X = 4
12.
13.
14.
y-intercept = −4
Y = 1
3X + 2
X − 3Y = 12�or�−X + 3Y = −12
slope = 26
= 13
−2X − X + 12 = X − 12
−3X + 12 = X − 12
24 = 4X
244
= X = 6
− 3 + 7( ) − 42 + −4( )2= 2R
−10 − 16 + 16 = 2R
10 − 16 + 16 = 2R
10 = 2R
102
= R = 5
9 18( ) −7
2Y +2 18( ) 2
9=6 18( ) −4
3
−63Y + 4 = −24
−63Y = −28
Y = −28 = 49
Y
X#3
26
#6
#8
2.
3.
4.
slope
Y X
X Y o
= =
= −
= −
− =
26
134
13
4
3 12
y-intercept
rr X Y
B C Y X
Y X
,
− + = −= − −
= − +
3 12
3 1
3 6
5.
6.
7.
:
see graph
33 6
3 4
3 4
X Y
Y X
X Y
+ =
= − −+ = −
8.
9.
10.
see graph
slopes are the same,
so lines are parallel
11. 6 3 4 7X X X− + = +55 3 4 7
4
2 12 123 12 12
24 4
X X
X
X X XX X
XX
+ = +=
− − + = −− + = −
==
12.
66
3 7 4 4 2
10 16 16 2
10 16 16 21
2 213. − +( ) − + −( ) =
− − + =− + =
R
R
R00 2
5
18 72
18 29
18 43
63 4 24
9 2 6
==
( ) − + ( ) = ( ) −
− + = −
RR
Y
Y
14.
−− = −
=
− ==
63 2849
100 60 40
40 12 900
Y
Y
of
aLGeBra 1
sYsteMatic reVieW 10c - sYsteMatic reVieW 10D
soLutions192
55 3 4 7
4
2 12 123 12 12
24 4
X X
X
X X XX X
XX
+ = +=
− − + = −− + = −
==
12.
66
3 7 4 4 2
10 16 16 2
10 16 16 21
2 213. − +( ) − + −( ) =
− − + =− + =
R
R
R00 2
5
18 72
18 29
18 43
63 4 24
9 2 6
==
( ) − + ( ) = ( ) −
− + = −
RR
Y
Y
14.
−− = −
=
− ==
63 2849
100 60 40
40 12 900
Y
Y
of
15.
16.
% % %
% $ , .440 12 900 5 160
15 3 153
153 5160 789 48
× ==
× =
, $ ,
. % .
. $ .
17.
118.
19.
. .
. $ .
25 2 125 12 12
8 125 1 00
÷ =
× =
or cents
or 44 .25 $1.00
dif
× =( )= + = =20. T W T total and W weeks5 3;
fferent letters may be used( )
Systematic Review 10D1.
2.
3.
4.
see graph
y-intercept
slope
Y X
= − = −
== −
63
2
1
2 ++ + =
= −
= −
−
1 2 1
12
1
12
1
2
; X Y
A Y X
Y X
X Y
5.
6.
7.
:
see graph
== − + = −
= +
− = − −
2 2 2
12
3
2 6
or X Y
Y X
X Y or
8.
9.
see graph
XX Y+ =2 6
10. slopes are the same,
so lines are paraallel
11. 2 2 2 3 3 103 2 2 7
5
X X X X XX X
X
+ − + = − + −+ = +
=
1.
2.
3.
4.
see graph
y-intercept
slope
Y X
= − = −
== −
63
2
1
2 ++ + =
= −
= −
−
1 2 1
12
1
12
1
2
; X Y
A Y X
Y X
X Y
5.
6.
7.
:
see graph
== − + = −
= +
− = − −
2 2 2
12
3
2 6
or X Y
Y X
X Y or
8.
9.
see graph
XX Y+ =2 6
10. slopes are the same,
so lines are paraallel
11. 2 2 2 3 3 103 2 2 7
5
X X X X XX X
X
+ − + = − + −+ = +
=
Y
X
#3
#6
3
-6
#8
12.
13.
3 1 2 1 4 2 3 12 3 46 2
3
6
Y Y Y Y YY Y
YY
− + − − = + + +− = +− =
= −
− +77 10 5 5
13 15 5
169 225 556 5
2 2
2 2
( ) + +( ) =
− ( ) + ( ) =− + =
=
M
M
MM
5565
11 15
60 53
60 94
60 65
10
20 15 12
=
=
( ) − = ( ) − + ( )−
M
M
A14.
00 135 7235 72
3572
100 55 45
45
= − +=
=
− =
AA
A
of
15.
16.
% % %
% $ ,
. , $ , .
. % .
.
9 645
45 9 645 4 340 25
15 3 153
153 4
=× =
=×
17.
,, . $ .
. .
340 25 664 06
2 50 25 10
10 2 20
10
≈
÷18.
19.
=× = bits
00 2 50
50 25 12 50
5
÷ =× =
= + = =. $ .
;20. L W L length and W weeeks
different letters may be used( )
aLGeBra 1
sYsteMatic reVieW 10e - Lesson Practice 11a
soLutions 193
Systematic Review 10E1.
2.
3.
4.
see graph
y-intercept
slope
Y X
= − = −
= −= −
11
1
1
−−+ = −
= −
1
1
2
X Y
C Y X5.
6.
:
see graph
Y
X
#6#3
-11
7.
8.
Y X
X Y or X Y
Y Y Y Y Y
Y
= −− = − + = −− − + + = + +
2
2 2
5 3 2 4 3 4 9 4
6 ++ = +− =
= −
− − − + = + − +− + = −
1 8 9
8 2
4
4 2 20 7 5 113 16
Y
Y
Y
M M M MM
9.44 18
25
3 4 5 2 3
10 2
10 25
39
MMW
W W
W
WW
+==
− − − + + =− =
==
10.
11. 66 134
36 299
36 512
117 116 15117 131
4 3( ) = ( ) + ( )= +=
=
B
BB
B 1131117
1 14117
100 48 52
52 25 813
B
of
=
− =12.
13.
% % %
% $ , ==× =
=×
. , $ , .
. % .
. ,
52 25 813 13 422 76
15 3 153
153 13 422
14.
.. $ , .76 2 053 68
20 12 240
5 20 100
≈
15.
16.
× =× =
pence
shiillings
C W
C cash and W weeks
17.
18.
= − += =
=
20 1000
100 110 10 10 100
36 6 6 6 36
144 12 12 12
× =( )= × =( )= × =
19.
20. 1144( )
= +=
=
B
BB
B 1131117
1 14117
100 48 52
52 25 813
B
of
=
− =12.
13.
% % %
% $ , ==× =
=×
. , $ , .
. % .
. ,
52 25 813 13 422 76
15 3 153
153 13 422
14.
.. $ , .76 2 053 68
20 12 240
5 20 100
≈
15.
16.
× =× =
pence
shiillings
C W
C cash and W weeks
17.
18.
= − += =
=
20 1000
100 110 10 10 100
36 6 6 6 36
144 12 12 12
× =( )= × =( )= × =
19.
20. 1144( )
Lesson Practice 11A1.
2.
3.
4.
see graph
y-intercept = −= −− =
1
3 1
3 1
Y X
X Y or −− + = −3 1X Y
Lesson Practice 10A 1. on the graph
2.
3.
4.
5.
6.
7.
8.
9.
10.
y-intercept = −1
Y = 3X − 1
3X − Y = 1�or�−3X + Y = −1
3 − 16 − −2( ) = 2
8= 1
4� see graph( )
Y = 14
X + b
3( ) = 14
6( ) + b
3 = 32
+ b
112
= b� see graph( )
Y = 1
4X + 11
2
Y − 14
X = 32
X − 4Y = −6�or�−X + 4Y = 6
2( ) = 5 1( ) + b
2 − 5 = b
−3 = b;�Y = 5X − 3
6( ) = 6 −3( ) + b
6 = −18 + b
24 = b;�Y = 6X + 24
1( ) ( )
Y
X
#1
#5,6
2
8
5.
6.
3 16 2
28
14
14
3 14
6
−− −( ) = = ( )
= +
( ) = ( )
see graph
Y X b
++
= +
= ( )
= +
− =
b
b
b
Y X
Y X
3 32
1 12
14
1 12
14
32
see graph
7.
8.
XX Y or X Y
bb
bY X
− = − − + =
( ) = ( ) +− =
= −= −
4 6 4 6
2 5 12 5
35 3
9.
100.
11.
6 6 3
6 18246 24
1 4 11
( ) = −( ) += − +== +
( ) = − ( ) +
b
bbY X
b== − +== − +
( ) ( )
45
4 5
2 12
2
2 1112
1
bbY X
b
bb
Y X
aLGeBra 1
Lesson Practice 11a - Lesson Practice 11B
soLutions194
= +
− =
b
b
b
Y X
Y X
3 32
1 12
14
1 12
14
32
see graph
7.
8.
XX Y or X Y
bb
bY X
− = − − + =
( ) = ( ) +− =
= −= −
4 6 4 6
2 5 12 5
35 3
9.
100.
11.
6 6 3
6 18246 24
1 4 11
( ) = −( ) += − +== +
( ) = − ( ) +
b
bbY X
b== − +== − +
( ) = ( ) += +=
= +
45
4 5
2 12
2
2 1112
1
bbY X
b
bb
Y X
12.
13..
14.
8 23
5
8 103
4 23
23
4 23
1 14
2
( ) = ( ) +
= +
=
= +
( ) = − ( )
b
b
b
Y X
++
= − +
=
= − +
−−
= = =
( ) =
b
b
b
Y X
m
1 12
1 1214
1 12
5 34 2
22
1
3 1 2
15.
(( ) += +== +
−−
= −−
= =
( ) = ( ) +
b
bbY X
m
3 21
1
1 62 4
52
52
1 52
2
16.
bb
bb
Y X
m
1 54
52
4
0 31 3
32
32
0 32
1
= += −
= −
−−
= −−
= =
( ) = ( ) +
17.
bb
b
b
Y X
0 32
32
32
32
= +
= −
= −
+= +== +
−−
= −−
= =
( ) = ( ) +
b
bbY X
m
3 21
1
1 62 4
52
52
1 52
2
16.
bb
bb
Y X
m
1 54
52
4
0 31 3
32
32
0 32
1
= += −
= −
−−
= −−
= =
( ) = ( ) +
17.
bb
b
b
Y X
0 32
32
32
32
= +
= −
= −
Lesson Practice 11B1.
2.
see graph
Estimates
2 12
3 2 32
12
( ) = ( ) + = + =b b b; ;
near 12
are acceptable.
Y
X
-7
6
#5,6
#1
3.
4.
5.
Y X
X Y or X Y
= +
− = − − + =− −− −( ) = −
12
12
2 1 2 1
2 52 4
76
ssee
Y X b
b
b b
graph( )
= − +
−( ) = − ( ) +
− = − +
6. 76
2 76
2
2 146
; == ( )
= − +
+ =
+ =
13
76
13
76
13
7 6 2
2
see graph
7.
8.
9.
Y X
Y X
X Y(( ) = ( ) += + = −= −
( ) = ( ) += +
8 1
2 8 6
8 6
2 3 1
2 3
b
b b
Y X
b
b
;
;
10.
bb
Y X
b
b b
Y X
= −= −
( ) = − ( ) += − + == − +
1
3 1
0 2 3
0 6 6
2 6
3
11.
12.
;
−−− −
= −−
=
( ) = −( ) +
= − + =
= +
52 2
24
12
3 12
2
3 22
4
12
4
b
b b
Y X
;
aLGeBra 1
Lesson Practice 11B - sYsteMatic reVieW 11c
soLutions 195
= − +
+ =
+ =
13
76
13
76
13
7 6 2
2
see graph
7.
8.
9.
Y X
Y X
X Y(( ) = ( ) += + = −= −
( ) = ( ) += +
8 1
2 8 6
8 6
2 3 1
2 3
b
b b
Y X
b
b
;
;
10.
bb
Y X
b
b b
Y X
= −= −
( ) = − ( ) += − + == − +
1
3 1
0 2 3
0 6 6
2 6
3
11.
12.
;
−−− −
= −−
=
( ) = −( ) +
= − + =
= +
52 2
24
12
3 12
2
3 22
4
12
4
b
b b
Y X
;
133. 1 21 5
14
14
1 14
1
1 14
34
14
3
−−
= −−
=
( ) = ( ) +
= + =
= +
b
b b
Y X
;
44
1 33 2
41
4
1 4 3
1 121
14. − −( )− − −( ) =
−= −
( ) = − −( ) += += −
b
bb 11
4 11
1 62 5
53
1 53
2
1
Y X
b
= − −
− − −( )− − −( ) =
−( ) = −( ) +
− = −
15.
1103
7353
73
6 31 5
96
32
6 32
+
=
= +
− −( )− −
=−
= −
( ) = − −
b
b
Y X
16.
11
6 3292
32
92
8 23 7
610
35
2
( ) +
= +
=
= − +
−− −
=−
= −
( )
b
b
b
Y X
17.
== − ( ) +
= − +
=
= − +
35
7
2 215
6 153
56 1
5
b
b
b
Y X
1103
7353
73
6 31 5
96
32
6 32
( ) = − −11
6 3292
32
92
8 23 7
610
35
2
( ) +
= +
=
= − +
−− −
=−
= −
( )
b
b
b
Y X
17.
== − ( ) +
= − +
=
= − +
35
7
2 215
6 153
56 1
5
b
b
b
Y X
Systematic Review 11C1.
2.
see graph on the next page
1 14
5
1 54
( ) = −( ) +
= −
b
++
=
= +
− = − − + =−
− −=
b
b
Y X
X Y or X Y
2 14
14
2 14
4 9 4 9
2 23 1
3.
4. 004
0
2 0 1
−=
( )( ) = ( ) +see graph on the next page
5. b;;
;
b
Y Y
=( )
= =
2
2 2
see graph
6.
1.
2.
see graph on the next page
1 14
5
1 54
( ) = −( ) +
= −
b
++
=
= +
− = − − + =−
− −=
b
b
Y X
X Y or X Y
2 14
14
2 14
4 9 4 9
2 23 1
3.
4. 004
0
2 0 1
−=
( )( ) = ( ) +see graph on the next page
5. b;;
;
b
Y Y
=( )
= =
2
2 2
see graph
6.
Y
X
#7
#1
#4,5
#9
7.
8.
slope see graph= − ( )( ) = − −( ) +
= +== −
2
5 2 1
5 23
b
bbY 22 3
2 3
13
1 13
3
XX Y
slope
++ =
= − ( )
( ) = − ( )
9.
10.
see graph
++
= − +
=
= − +
+ =
b
b
b
Y X
X Y
1 33
213
2
3 6
aLGeBra 1
sYsteMatic reVieW 11c - sYsteMatic reVieW 11D
soLutions196
7.
8.
slope see graph= − ( )( ) = − −( ) +
= +== −
2
5 2 1
5 23
b
bbY 22 3
2 3
13
1 13
3
XX Y
slope
++ =
= − ( )
( ) = − ( )
9.
10.
see graph
++
= − +
=
= − +
+ =
b
b
b
Y X
X Y
1 33
213
2
3 6
11.
12.
distributive
commmutative
commutative
associative
13.
14.
15.
16.
9 3=445 45 45 98 44 10
51
51
5
% . ; . .= × =
=17.
18.
boysgirl
boyystotal
boys
656
56
5 6 83 83
56
48 408
. %
=
= =
× =
19.
20.
÷ ≈
Systematic Review 11D1.
2.
3.
on the graph
1 25
1
1 25
75
25
( ) = − ( ) +
= − +
=
= −
b
b
b
Y X ++
+ =−
− −( ) = − = − ( )
(
1 25
2 5 7
2 43 1
24
12
2
X Y
4.
5.
see graph
)) = − ( ) +
= − +
=
= − +
+ =
12
3
2 32
3 12
12
72
2 7
b
b
b
Y X
X Y
6.
++
+ =−
− −( ) = − = − ( )
(
1 25
2 5 7
2 43 1
24
12
2
X Y
4.
5.
see graph
)) = − ( ) +
= − +
=
= − +
+ =
12
3
2 32
3 12
12
72
2 7
b
b
b
Y X
X Y
6.
Y
X
#9
#7
#4, #5
#1
7.
8.
slope see graph= − ( )
−( ) = − ( ) +
− = − +
13
3 13
3
3 33
b
b
b == −
= − −
+ = −
= − ( )
(
213
2
3 6
32
1
Y X
X Y
9.
10.
slope see graph
)) = − ( ) +
= − +
=
= − +
+ =
32
2
1 62
432
4
3 2 8
b
b
b
Y X
X Y
11.
12.
true
faalse
false13.
14.
15.
16.
true
49 7
16 16
16 32 5 1
==× =
% .
. . 22
58
58
5 8 625 62 5
3
17.
18.
. . %
Steelertotal
Eagl
=
= =÷
eetotal
Eagle
838
3 8 375 37 5
375 640 240
. . %
.
=
= =× =
÷
19.
.
fans
Steeler fans625 640 400× =may also be compuuted with fractions( )= ( ) += +
20. Y
Y
Y
20 15 100
300 100
== $400
aLGeBra 1
sYsteMatic reVieW 11D - sYsteMatic reVieW 11e
soLutions 197
true
49 7
16 16
16 32 5 1
==× =
% .
. . 22
58
58
5 8 625 62 5
3
17.
18.
. . %
Steelertotal
Eagl
=
= =÷
eetotal
Eagle
838
3 8 375 37 5
375 640 240
. . %
.
=
= =× =
÷
19.
.
fans
Steeler fans625 640 400× =may also be compuuted with fractions( )= ( ) += +
20. Y
Y
Y
20 15 100
300 100
== $400
Systematic Review 11E1.
2.
3.
see graph
−( ) = − ( ) +− = − +
== − ++ =
1 1 41 4
3
3
bb
b
Y X
X Y 33
5 24 1
35
35
2 35
1
2
4.
5.
−− −
=−
= − ( )
( ) = − ( ) +
=
see graph
b
−− +
= ( )
= − +
+ =
35
135
35
2 35
3 5 13
b
b
Y X
X Y
see graph
6.
1.
2.
3.
see graph
−( ) = − ( ) +− = − +
== − ++ =
1 1 41 4
3
3
bb
b
Y X
X Y 33
5 24 1
35
35
2 35
1
2
4.
5.
−− −
=−
= − ( )
( ) = − ( ) +
=
see graph
b
−− +
= ( )
= − +
+ =
35
135
35
2 35
3 5 13
b
b
Y X
X Y
see graph
6.
Y
X#9
#7
#4, #5
#1
7.
8.
slope
b
bbY
= − ( )( ) = − −( ) +
= +== −
1
3 1 2
3 21
see graph
XX
X Y
slope
++ =
= − ( )
( ) = − −( ) +
1
1
14
3 14
1
9.
10.
see graph
bb
b
b
Y X
X Y
3 1411414
2 34
4 11
1 2 3 4
= +
=
= − +
+ =
− { }
7.
8.
slope
b
bbY
( ) = − −( ) += +== −
1
3 1 2
3 21
see graph
XX
X Y
slope
++ =
= − ( )
( ) = − −( ) +
1
1
14
3 14
1
9.
10.
see graph
bb
b
b
Y X
X Y
3 1411414
2 34
4 11
1 2 3 4
= +
=
= − +
+ =
−( )( ) −( )( )11. −−( ) = − − − −( ) { }−( ) −( )( ) =
( )( ) ==
5
2 12 25
24 25
2X
X
X
X 6600
72 84 36
12 6 7 12 3
6 7 31 3
12. A A AF
A A F
FF
F
− =−( ) = ( )− =− =
== −
−( ) − ( ) = −( )− − = −
−
13
10 4 2 10 1 8 10 6
42 18 60
6
13. . .Q Q
Q Q
00 60
1
1000 14 1000 023 1000 07
140
Q
Q
C
= −=
( ) − ( ) = ( )14. . . .
−− ==
=
=
= =
23 70117 7011770
1 4770
25
2 5 4 40
CC
C
C
15.
1
; . %÷
66.
17.
18.
1
35
3 5 6 60
4 500 200
500 200 300
; . %
.
÷ = =
× =− =
g
g
99.
20.
5 280 4 5 23 760
1 3 5 280 3 1 760
, . , ft
ft; , ,
× == =yd ÷ yyd
aLGeBra 1
Lesson Practice 12a - Lesson Practice 12B
soLutions198
Lesson Practice 12A1. 3 9 1
33Y X Y X= + => = + ; see graph
Y
X
2.
3.
solid
true0 0 0 0 9 0 9
0 4
, ; ;
,
: 3
: 3
( ) ( ) ( ) +( )
≤ ≤
44 0 9 12 9( ) ( ) +≤ ≤; ;
You may choose any point
false
ss you wish,
as long as they are on opposite siddes
of the line.
graph
see gra
4.
5.
see
Y X= − −12
2; pph
Y
X
6.
7.
dotted
true0 0 0 0 4 0 4
0 3
, ; ;
, –
: 2
( ) ( ) ( ) − −(
> – >
)) −( ) ( ) − −
= −
: 2 –6
see graph
3 0 4 4
3
> – >; ; false
Y
8.
9. XX +1; see graph
Y
X
10.
11.
solid
X Y
false
3
0 0 0 0 1
0
+( ) ( ) ( ), ; ;
,
: 3 0 + ≥1 ≥
: 3 2
see graph
2 0 2 1( ) ( ) ( )
> −
+ ≥1 ≥; ; true
Y X
12.
13. −−− < − + > −
2
2 4 6 2 314. Y X Y X;
Remember that multiplyingg or dividing
an inequality by a negative numberr
reverses the direction of the inequality.
15. −44 8 8 2 2Y X Y X≥ ≥+ − −;
Lesson Practice 12B1. Y X= −2 3; see graph
Y
X
2.
3.
solid
:
0 0 2 0 0 3 0 3
3 0
, ; ;
,
( ) − ( ) + ( ) − −(
≤ ≤ false
)) − ( ) + ( ) − − −:
You may choose any
; ;2 3 0 3 6 3≤ ≤ true
points you wish,
as long as they are on opposiite sides
of the line.
see graph4.
Y
X
aLGeBra 1
Lesson Practice 12B - sYsteMatic reVieW 12c
soLutions 199
5.
6.
7.
Y X
solid
= −
( ) ( ) ( ) −
23
3
0 0 3 0 2 0
;
,
see graph
: ≤ 99 0 9
0 4 3 4 2 0 9 12 9
; ;
, ; ;
≤
≤ ≤
−
−( ) −( ) ( ) − − −
false
tr
:
uue
8. see graph
Y
X
9.
10.
11.
Y X
dotted
= +
( ) − ( ) +
15
1
0 0 0 5 0
;
,
see graph
: (( ) > >( ) − ( ) + ( ) > >
5 0 5
0 2 0 5 2 5 10 5
; ;
, ; ;
false
tru : ee
Y X
Y X
Y X
12.
13.
14.
15.
see graph
mult
< −− > − +< −
3 5
3 5
3 5
iiplying or dividing
by a negative number
Systematic Review 12C 1.
2.
3.
se
dotted
e graph
:0 0 0 2 0 1 0 1, ;( ) − ( ) > − ( ) − > − ;;
, ; ;
true
:
on t
0 2 2 2 0 1 2 1( ) − ( ) > − ( ) − − > − false
4. hhe graph
: true
Or, ch
5. yes ; ;− −( ) > − ( ) − > −2 2 3 1 2 7
eeck visually on the graph
see graph 6.
Y
X
7.
8.
solid
false0 0 0 0 3 0 3
4 0
, ; ;
,
:
:
( ) ( ) ( ) − −( )
≤ ≤
00 4 3 0 1( ) ( ) −≤ ≤; ; true
9. see graph
Y
X
10.
1
multiplying or dividing
by a negative number
11.
12.
13
WF
WF
WF
WF or
× =
=
× =
=
16 1
116
2000 1
12000
0005.
..
14.
15.
16.
− = − +
= −
=
= −
2 3 5
32
52
32
23
Y X
Y X
slope
slope
y-iintercept == − − =× =
2
2 2 2 2
16 242 38 72
Y X or X Y
. .17.
18. qquadrant 3
19.
20
11 6
10
1 1 6 10
16
..
=
( )( ) = ( )( )=
XX
X km
.. 11 6 101 10 1 6
6 25
..
.
=
( )( ) = ( )( )=
X
X
X mi
aLGeBra 1
sYsteMatic reVieW 12c - sYsteMatic reVieW 12e
soLutions200
== − − =× =
2
2 2 2 2
16 242 38 72
Y X or X Y
. .17.
18. qquadrant 3
19.
20
11 6
10
1 1 6 10
16
..
=
( )( ) = ( )( )=
XX
X km
.. 11 6 101 10 1 6
6 25
..
.
=
( )( ) = ( )( )=
X
X
X mi
Systematic Review 12D1.
2.
3.
see graph
:
Y
dotted
= −( )
( ) ( ) + < <
2
0 0 0 2 0 2, ; 00
0 3 3 2 0 1 0
;
, ; ;
false
true−( ) −( ) + < − <:
see grap4. hh
Y
X
5.
6.
7.
8
4 8 2
13
2
Y Y
Y X
dotted
< − < −
= +
;
see graph
.. 0 0 0 3 13
0 1 3 1
0 3 3
, ; ;
,
:
:
( ) ( ) − > ( ) − − > −
( ) (false
)) − > ( ) − > −
< −
3 13
0 1 0 1
2 1
; ;
true
Y X
9.
10.
see graph
Y
X
11.
12.
13.
WF WF
WF
WF
× = =
× =
= =
60 1 160
7 1
17
14 14
145
;
. %
.
≈
==
( )( ) = ( )( )=
=
( )( ) =
10
1 45 10
4 5
145 2
1 2
X
X
X kg
X
.
.
.
.
14.
445
4 44
6 4 3 06 4 3
46
36
2
( )( )X
X lb
Y XY X
Y X
Y
.
11.
12.
13.
WF WF
WF
WF
× = =
× =
= =
60 1 160
7 1
17
14 14
145
;
. %
.
≈
==
( )( ) = ( )( )=
=
( )( ) =
10
1 45 10
4 5
145 2
1 2
X
X
X kg
X
.
.
.
.
14.
445
4 44
6 4 3 06 4 3
46
36
2
( )( )=
− − == +
= +
=
X
X lb
Y XY X
Y X
Y
.
15.
3312
46
2332
1 12
1
1 12
X
m
slope
b
b
+
= =
= −
( ) = − ( ) +
= − +
16.
17.
bb
Y X or X Y
N N
=
= − + + =
= =−
32
12
32
2 3
9 25 36 36
6 5
. %18.
19.
÷
++( ) − ( ) + = − + =
8
6 10 5 10 8 60 50 8 1820.
Systematic Review 12E1.
2.
3.
on the graph
:
solid
0 0 0 2 0 3 0 3, ;( ) ( ) ( ) +≤ ≤ ;;
, ; ;
true
false−( ) ( ) −( ) + −3 0 0 2 3 3 0 3 :
on th
≤ ≤
4. ee graph
:
5. yes
tru;
1 2 3 3
1 6 3
1 9
( ) ( ) ++
≤
≤
≤ ee
aLGeBra 1
sYsteMatic reVieW 12e - Lesson Practice 13a
soLutions 201
Y
X
6.
7.
8.
on the graph below
:
solid
fals0 0 0 4, ;( ) ( ) ≥ ee
true6 0 6 4, ;( ) ( ):
on the graph below
mul
≥
9.
10. ttiplying or dividing
by a negative number
Y
X
11.
12.
13.
WF
WF
WF
WF
q
× =
=
× =
= = =
=
8 1
18
4 1
14
25 25
195
4
. %
.tt
X
X
X liters
X
1 95 4
3 8
195 1
1 1
( )( ) = ( )( )=
=
( )( ) =
.
.
.14.
..
.
95
1 119
1 05
12
16
2 32
( )( )=
= +
= +=
X
X quarts
Y X
Y Xm
≈
15.
22
12
4 3 3
4 95
3 5 3
16.
17.
m
b
bb
Y X or X
= −
−( ) = −( ) +− = − +
== + −− = − − + =
=× =
Y X Y5 3 5
12 17 71 71
17 425 72
or
. %
. .
18.
19.
÷ ≈
225
420. quadrant
8 1
18
4 1
14
25 25
195
4
. %
.tt
X
X
X liters
X
1 95 4
3 8
195 1
1 1( )( ) = ..
.
95
1 119
1 05
12
16
2 32
( )( )=
= +
= +=
X
X quarts
Y X
Y Xm
≈
15.
22
12
4 3 3
4 95
3 5 3
16.
17.
m
b
bb
Y X or X
= −
−( ) = −( ) +− = − +
== + −− = − − + =
=× =
Y X Y5 3 5
12 17 71 71
17 425 72
or
. %
. .
18.
19.
÷ ≈
225
420. quadrant
Lesson Practice 13A
1.
2.
3.
4.
on the graph
on the graph
1, 2
on the gr
( )aaph
on the graph5.
6. 3 4,−( )
Y
X
a
b
d c
7.
8.
9.
10.
on the graph
on the graph
on the
−( )3 2,
ggraph
on the graph
11.
12. 3 1,( )
Y
X
g
e
h
f
13.
14.
15.
16.
on the graph
on the graph
on th
1 1,( )ee graph
on the graph17.
18. − −( )1 3,
Y
X
r
sj k
aLGeBra 1
Lesson Practice 13B - sYsteMatic reVieW 13c
soLutions202
Lesson Practice 13B
1.
2.
3.
4.
on the graph
on the graph
on t
0 52
,
hhe graph
on the graph5.
6. − −( )2 1,
Y
X
b
d
a
7.
8.
on the graph
on the graph
Y X
Y X
= −( )
= − +
2
13
2
( )
= − −( )
9.
10.
11.
3 1
2 2
,
on the graph
on the
Y X
graph
12. −( )3 4,
Y
X
f
g
e
h
13.
14.
15
on the graph
on the graph
Y X= − +
14
3
..
16.
17.
0 3
12
1
,
on the graph
on the
( )
= − −
Y X
graph
18. 2 2,−( )
Y
X
r
s
j
k
Systematic Review 13C1.
2.
on the graph
on the graph
Y
X
ba
3.
4.
5.
−( )−( ) = − ( ) +− = − +
== − ++ =
1 2
3 4 1
3 41
4 1
4
,
b
bb
Y X
X Y 11
5 15 5
610
35
1 35
5
1 155
1 3
6.
7.
− −− −
= −−
= =
( ) = ( ) +
= +
= +
m
b
b
bbb
Y X
Y X
X Y or X Y
= −
= −
= −− + = − − =
2
35
2
5 3 10
3 5 10 3 5 10
8.
9. mm
b
b
b
b
Y X
Y
=
( ) = ( ) +
= +
− =
=
= +
=
23
4 23
4
4 83
4 8343
23
43
3 2
10.
XX
X Y or X Y
X X XX X
+− + = − = −
− + = +− = −
4
2 3 4 2 3 4
8 3 7 4 85 4 8
11.77
1
4 12 20
4 3 4 5
3 5
2
5 5 3 72
X
Q
Q
Q
Q
X
=
+ =+( ) = ( )+ =
=
+ +
12.
13. ÷ (( ) = ++ + = ++ + = +
+ = +
2 2725 5 3 21 2 27
5 3 21 2 273 26 2
XX XX XX X
÷
22727 26 1
7 2 4 11 3 249 2 4 44 3 2
2
X
Y YY Y
= − =
× − +( ) = −× − − = −
14.
998 4 44 3 254 3 4 256 7
8
30 610
33 10
− − = −= + −==
( ) −
Y YY YY
Y
15. 00 23
30 111
18 20 33020 312
31220
15
30( ) = ( )− =− =
=−
= −
X
XX
X
335
15 6
8 4 6 32 8
12 6 32 812 6 4
12
or
Y
YY
aLGeBra 1
sYsteMatic reVieW 13c - sYsteMatic reVieW 13D
soLutions 203
771
4 12 20
4 3 4 5
3 5
2
5 5 3 72
X
Q
Q
Q
Q
X
+ ==
+ +
12.
13. ÷ (( ) = ++ + = ++ + = +
+ = +
2 2725 5 3 21 2 27
5 3 21 2 273 26 2
XX XX XX X
÷
22727 26 1
7 2 4 11 3 249 2 4 44 3 2
2
X
Y YY Y
= − =
× − +( ) = −× − − = −
14.
998 4 44 3 254 3 4 256 7
8
30 610
33 10
− − = −= + −==
( ) −
Y YY YY
Y
15. 00 23
30 111
18 20 33020 312
31220
15
30( ) = ( )− =− =
=−
= −
X
XX
X
335
15 6
8 4 6 32 8
12 6 32 812 6 4
12
or
Y
YY
−
− − − = −− − =
− =−
.
16. ÷
÷
44 68 686
1 13
3
==
=
=
YY
Y
Y
hours17. 7:45 to 2:15 is 6 12
338 6 5 52
338 13 26
32 64 128
÷
÷
.
, ,
==
mph
mpg18.
19. douuble each number
add the previous tw
( )20. 8 13, oo numbers( )
Systematic Review 13D1.
2.
on the graph
on the graph
Y
X
b
a
3.
4.
5.
4 1
1 32
1
1 32
12
32
12
3
,−( )( ) = − −( ) +
= +
= −
= − −
b
b
b
Y X
X ++ = −− −− −( ) = −
= −
2 1
4 21 4
65
65
2 65
4
2 2
Y
m
b
6.
7.
3.
4.
5.
4 1
1 32
1
1 32
12
32
12
3
,−( )( ) = − −( ) +
= +
= −
= − −
b
b
b
Y X
X ++ = −− −− −( ) = −
= −
( ) = − −( ) +
=
2 1
4 21 4
65
65
2 65
4
2 2
Y
m
b
6.
7.
445145
65
145
6 5 14
43
3 43
+
= −
= − −
+ = −
= −
−( ) = −
b
b
Y X
X Y
m
8.
9.
22
3 83
93
83
13
43
13
4 3 1
( ) +
− = − +
− + =
= −
= − −
+ = −
b
b
b
b
Y X
X Y
10.
111.
12.
16 8 568 56
568
7
18 15 24
3 6 5 3 8
X XX
X
A
A
− ==
= =
− =−( ) = (( )− =
=
= =
−( ) − + = −
−( ) −
6 5 86 13
136
2 16
1 7 8 11 3
6
2
2
AA
A
N13.
88 3 11
36 8 148 50
508
6 14
100 78
N
NN
N
= − −− = −− = −
= −−
=
( )14. . ++ ( ) = ( )+ =
=
= =
100 4 100 2
78 40 200118 200
118200
591
. X
XX
X000
59
3 12
2 1 8
3 5 2 1 8
10 3 1
.
. .
. . .
.
or
A A
A A
aLGeBra 1
sYsteMatic reVieW 13D - sYsteMatic reVieW 13e
soLutions204
10.
111.
12.
16 8 568 56
568
7
18 15 24
3 6 5 3 8
X XX
X
A
A
− ==
= =
− =−( ) = (( )− =
=
= =
−( ) − + = −
−( ) −
6 5 86 13
136
2 16
1 7 8 11 3
6
2
2
AA
A
N13.
88 3 11
36 8 148 50
508
6 14
100 78
N
NN
N
= − −− = −− = −
= −−
=
( )14. . ++ ( ) = ( )+ =
=
= =
100 4 100 2
78 40 200118 200
118200
591
. X
XX
X000
59
3 12
2 1 8
3 5 2 1 8
10 3 1
.
. .
. . .
.
or
A A
A A
15. + = −
+ = −( ) + 00 5 10 2 10 1 8
3 5 20 1821 15
2115
1
. .A A
A AA
A
( ) = ( ) − ( )+ = −
=
= = 225
4 8 6 3 5 7
4 6 3 25 716 6 75 7
2 2
2
16. −( ) × − × =
−( ) × − × =× − =
Y
YY
996 75 721 7217
3
− ==
= =
YY
Y
17. 6:50 AM to 2:05 PM is 7..25 hours
3
348 7 25 48
348 14 5 24
÷
÷
.
.
==
mph
mpg18.
19. 66, 49, 64, 81 count by 1, and square( )20. 1
162, ,1
4861
1458
multiply previous number by 13
Systematic Review 13E1.
2.
on the graph
on the graph
Y
X
a
b
3.
4.
5.
3 3
2 1 5
2 53
3
3
, ( )( ) = ( ) +
= += −
= −− = −
b
bb
Y X
X Y or X ++ = −
= −−
= −−
=
( ) = ( ) +
= +
=
Y
m
b
b
b
3
4 51 3
12
12
4 12
1
4 12
3 1
6.
7.
22
12
72
2 7
2 7 2 7
54
2
8.
9.
Y X
Y X
X Y or X Y
m
= +
= +− = − − + =
=
−( ) = 554
2
2 104
84
104
24
12
54
12
4
−( ) +
− = − +
− + =
= =
= +
b
b
b
b
Y X
Y
10.
== +− = − − + =
+ + − − = − + +
5 2
5 4 2 5 4 2
3 7 2 5 4 1
X
X Y or X Y
Q Q Q Q11. QQ
Q
Q
T T T T T TT
T
++ =
=
+ + − − = + − − +− =
4
2 5
3
4 3 6 2 2 5 4 1 22 2 4
2
12.
==
= =
− + =−( ) + ( )
662
3
2 8 06 5 72
100 2 8 100 06
T
P P
P P
13. . . .
. . == ( )− + =
− =
=−
= −
100 5 72
280 6 572274 572
572274286
.
P PP
P
P1137
32 8 3624 36
3624
1 12
03 34
aLGeBra 1
sYsteMatic reVieW 13e - Lesson Practice 14a
soLutions 205
554
2
2 104
84
104
24
12
54
12
4
+
− = − +
− + =
= =
= +
b
b
b
b
Y X
Y
10.
== +− = − − + =
+ + − − = − + +
5 2
5 4 2 5 4 2
3 7 2 5 4 1
X
X Y or X Y
Q Q Q Q11. QQ
Q
Q
T T T T T TT
T
++ =
=
+ + − − = + − − +− =
4
2 5
3
4 3 6 2 2 5 4 1 22 2 4
2
12.
==
= =
− + =−( ) + ( )
662
3
2 8 06 5 72
100 2 8 100 06
T
P P
P P
13. . . .
. . == ( )− + =
− =
=−
= −
100 5 72
280 6 572274 572
572274286
.
P PP
P
P1137
32 8 3624 36
3624
1 12
03 34
14.
15.
Y YY
Y
− = −= −
= − = −
( ) . ( ) − =
( )( )( ) − =− =
X
X
X
.
. . .
. .
75 0
03 75 75 0
0225 75 0
100 000 0225 10 000 75
225 75007500225
3
, . , .( ) = ( )=
=
=
X
X
X
X 33 13
33 33
4 23
3 13
3
143
103
3
3 143
.or
X
X
16. + = −
+ = −
+
= −( )
+ = −= −
= −
= −
3 103
3 3
14 10 910 23
2310
2
X
XX
X
X 3310
2 3
335 193
.or
hours
−
17. 8:20 to 2:40 is 6 13
÷ == ×
=
335 319
52 9
335 13 4 25
≈
÷
.
.
, ,
mph
mpg
XD XE
18.
19. XXF (X times the next letter
in the alphabet)
20.. 4 75 5 5 25 5 5 5 75. , , . , . , . (add .25 each time)
Lesson Practice 14A1.
2.
4 2,
replace X in equation 2
with its equi
−( )
vvalent, Y
Y Y
YY
+( )+( ) + = −
= −= −
6
6 3 2
4 82
:
Y
X
3. replace Y in equation 1
with its equivalent, −22
2 6
4
2 3 0 23
2 7 12
( )= −( ) +=
+ = => = −
− = => =
:
X
X
X Y Y X
X Y Y
4.
XX −
−( )
72
3 2,
Y
X
5. replace X in equation 1
with its equivalent, 7 ++( )+( ) + =+ + =
= −= −
2
2 7 2 3 014 4 3 0
7 142
Y
Y YY Y
YY
:
aLGeBra 1
Lesson Practice 14a - Lesson Practice 14B
soLutions206
6. replace Y in equation 1
with its equivalent, −22
2 3 2 02 6 0
2 63
( )+ −( ) =
− ===
:
XX
XX
Y
X
7.
8.
X Y Y X+ = => = − +
( )2 10 1
25
4 3,
replace Y in equationn 2
with its equivalent, :2 5
2 2 5 10
4
X
X X
X
−( )+ −( ) =+ XX
XX
− ===
10 105 20
4
9. replace X in equation 1
with itts equivalent, 4 :
replace
( )= ( ) −= −=
YYY
2 4 58 53
10. YY in equation 1
with its equivalent, :X
X
+( )−
3
2 3 XX
X XXX
+( ) = −− − = −
− == −
3 4
2 3 9 45
5
replace X in equationn 2
with its equivalent, :−( )= −( ) += −
− −
5
5 3
2
5
Y
Y
, 22( )
Lesson Practice 14B1.
2.
−( )
+ = => = − +
1 2
1 1
,
equation 1 for X:solve
X Y X Y
rreplace X in equation 2
with its equivalent, −Y ++( )= − +( ) += − +==
1
1 34
2 42
:
Y YY YYY
Y
X
3. replace Y in equation 2
with its equivalent, 2(( )( ) = +− =
:
2 31
XX
Y
X
4.
5.
2 4 2 4
5 6
X Y Y X− = => = −( ),
solve equation 2 for X:
YY X X Y= − + => = − +11 11
replace X in equation 1
with itss equivalent, :− +( )− +( ) − =− + − =
−
Y
Y YY Y
11
2 11 42 22 4
3YYY= −=
186
aLGeBra 1
Lesson Practice 14B - sYsteMatic reVieW 14c
soLutions 207
6. replace Y in equation 2
with its equivalent, 6(( )( ) = − +− = −
=
:
6 11
55
X
XX
Y
X
7.
8.
2 1 2 1
1 3
X Y Y X+ = − => = − −−( ),
solve equation 2 for XX:
replace X in equation 1
with its
Y X Y X= − => − =3 13
equivalent, :−
− + = −
− +
13
2 13
1
23
Y
Y Y
Y Y == −
= −
= −
1
13
1
3
Y
Y
9. replace Y in equation 2
with its equivalent, 3 :
change equatio
−( )−( ) = −
=3 3
1
X
X
10. nn 2 to
slope-intercept form:
rep
5 30 5 30X Y Y X− = => = −llace Y in equation 1
with its equivalent, 5X −30(( )+ −( ) =+ − =
==
:
replace
2 3 5 30 29
2 15 90 2917 119
7
X X
X XXX
X in equation 2
with its equivalent, 7 :( )( ) −5 7 YY
YYY
=− =− = −
=
3035 30
55
nn 2 to
slope-intercept form:
rep
5 30 5 30X Y Y X
llace Y in equation 1
with its equivalent, 5X −30(( )+ −( ) =+ − =
==
:
replace
2 3 5 30 29
2 15 90 2917 119
7
X X
X XXX
X in equation 2
with its equivalent, 7 :( )( ) −5 7 YY
YYY
=− =− = −
=
3035 30
55
Systematic Review 14C1.
2.
3 4,
replace Y in equation 2
with its equiv
( )
aalent, X :
replace X
+( )+( ) = −+ = −
=
1
1 2 21 2 2
3
X XX X
X
3. iin equation 1
with its equivalent, :3
3 1
( )= ( ) +Y
Y == 4
Y
X
line bline a
For #1–3.
4.
5.
−( )
− = => = +
1 3
4 4
,
solve equation 1 for Y:
r
Y X Y X
eeplace Y in equation 2
with its equivalent, X + 4(( )+( ) + =
= −= −
:
X XXX
4 2 13 3
1
6. replace X in equation 11
with its equivalent, −( )− −( ) =
+ ==
1
1 41 4
3
:
YY
Y
aLGeBra 1
sYsteMatic reVieW 14c - sYsteMatic reVieW 14D
soLutions208
Y
X
line d line c For #4–6.
7.
8.
m
b
b
b
b
= −−
= −−
=
( ) = ( ) +
− =
− =
=
3 51 4
23
23
3 23
1
3 23
93
23
773
23
73
3 2 7
2 3 7 2 3 7
4
9.
10.
Y X
Y X
X Y or X Y
m
= +
= +− = − − + =
= −33
2 43
2
2 83
2 83
63
83
143
11.
12.
( ) = − ( ) +
= − +
+ =
+ =
=
b
b
b
b
b
Y == − +
= − ++ =
43
143
3 4 14
4 3 14
X
Y X
X Y
13. 1, 4, 9, 16, 25, 336, 49, 64, 81,
100, 121, 144, 169, 196, 225
12,
2 3 4 5 6 7 8 9
10 11 12
2 2 2 2 2 2 2 2
2 2 2
, , , , , , , ,
, , ,
Depending on the sou
13 14 15
820
2 2 2, ,
14. miles
rrce, answers may vary.
If a different ddistance is used, answers for
#15 and 116 will also vary.
15. 820 50 16 4
16 410
16
÷ =
=
. hours
22460
16 24
7 23
, minor hr
16:24 :35 :59; 11:59 P+ = MM
16.
17.
820 25 32 8
32 8 1 269 41 62
92
÷ =× =
.
. . $ .
.
gallons
33
2 3
6 2 3 4 2 2
2 2 3
== − +
= − ++ =
43
143
3 4 14
4 3 14
X
Y X
X Y
13. 1, 4, 9, 16, 25, 336, 49, 64, 81,
100, 121, 144, 169, 196, 225
12,
2 3 4 5 6 7 8 9
10 11 12
2 2 2 2 2 2 2 2
2 2 2
, , , , , , , ,
, , ,
Depending on the sou
13 14 15
820
2 2 2, ,
14. miles
rrce, answers may vary.
If a different ddistance is used, answers for
#15 and 116 will also vary.
15. 820 50 16 4
16 410
16
÷ =
=
. hours
22460
16 24
7 23
, minor hr
16:24 :35 :59; 11:59 P+ = MM
16.
17.
820 25 32 8
32 8 1 269 41 62
92
÷ =× =
.
. . $ .
.
gallons
33
2 3
6 2 3 4 2 2
2 2 3
2 218.
19.
20.
A A A
prime
− +
= × = ×= × × =
;
LCM 112
Systematic Review 14D1.
2.
X Y Y X+ = − => = − −− −( )
6 6
4 2,
replace Y in equation 22
with its equivalent, 2 6
2 6 6
3 12
X
X X
X
+( )+ +( ) = −
= −
:
XX = −4
3. replace X in equation 1
with its equivalennt, −( )= −( ) += − += −
4
2 4 68 62
:
YYY
Y
X
line d
line cline b
line a
aLGeBra 1
sYsteMatic reVieW 14D - sYsteMatic reVieW 14e
soLutions 209
4.
5.
− −( )
− = => = +
3 2
2 4 2
,
solve equation 2 for Y:
Y X Y X 44
2
replace Y in equation 1
with its equivalent, XX
X XXX
+( )+( ) + = −
= −= −
4
2 4 53 9
3
:
replace X in equat6. iion 1
with its equivalent, :−( )+ −( ) = −
= −
3
3 5
2
Y
Y
7. mm
b
bb
Y X
X Y
= −− −
= −
( ) = − ( ) += +=
= −+ =
4 02 0
2
0 2 0
0 00
2
2 0
8.
9.
110.
11.
12.
m
b
b
b
b
Y X
=
( ) = ( ) +
− =
− =
=
=
34
2 34
2
2 64
84
64
12
34
++
= +− = − − + =
12
4 3 2
3 4 2 3 4 2
Y X
X Y or X Y
13. 1, 4, 9, 16, 225, 36, 49, 64, 81,
100, 121, 144, 169, 196, 2255
1
2, , , , , , , , ,
, ,
2 3 4 5 6 7 8 9
10 11
2 2 2 2 2 2 2 2
2 2 112 13 14 15
380
2 2 2 2, , ,
(See note for l14. miles eesson 14C.)
15. 380 50 7 6
7 610
7 3660
7
÷ =
=
. hours
or hhr, min36
6 13
380 25 15
7:36 :14 :50; 1:50 PM+ ==16. ÷ ..
. $ .
.
2
1 199 18 22
321
9 27 81
gallons
15.2× =
+ −
17.
18. A B ==+ −( ) = ( )+ − =
× = × ×
18
9 3 9 9 2
3 9 2
5 87 5 3 29
8
C
A B C
A B C
19.
20.
15. 380 50 7 6
7 610
7 3660
7
÷ =
=
. hours
or hhr, min36
6 13
380 25 15
7:36 :14 :50; 1:50 PM+ ==16. ÷ ..
. $ .
.
2
1 199 18 22
321
9 27 81
gallons
15.2× =
+ −
17.
18. A B ==+ −( ) = ( )+ − =
× = × ×
18
9 3 9 9 2
3 9 2
5 87 5 3 29
8
C
A B C
A B C
19.
20.
Systematic Review 14E1.
2.
−( )
+ = − => = − −
5 1
4 4
,
solve equation 1 for Y:
X Y Y XX
replace Y in equation 2
with its equivalent, −44
4 6
4 62 4 6
2 105
−( )− − −( ) = −+ +( ) = −
+ = −= −= −
X
X X
X XX
XX
:
3. rreplace X in equation 1
with its equivalent, −5(( )−( ) + = −
=−( )
:
,
5 4
1
1 0
Y
Y
4.
Y
X
c
d
a
b
5. solve
Y X Y X
equation 1 for Y:
replace
− = => = +4 4 4 4
YY in equation 2
with its equivalent, 4 4
4
X
X
+( )+
:
44 2 26 4 2
6 61
( ) + = −+ = −
= −= −
XX
XX
6. replace X in equatioon 1
with its equivalent, −( )− −( ) =
+ ==
1
4 1 44 4
:
YY
Y 00
2 13 1
34
1 34
1
1 34
44
34
7.
8.
m
b
b
= − −− −( ) = −
( ) = − −( ) +
= +
− =
aLGeBra 1
sYsteMatic reVieW 14e - Lesson Practice 15a
soLutions210
solve
Y X Y X
equation 1 for Y:
replace
4 4 4 4
YY in equation 2
with its equivalent, 4 4
4
X
X
+( )+
:
44 2 26 4 2
6 61
( ) + = −+ = −
= −= −
XX
XX
6. replace X in equatioon 1
with its equivalent, −( )− −( ) =
+ ==
1
4 1 44 4
:
YY
Y 00
2 13 1
34
1 34
1
1 34
44
34
7.
8.
m
b
b
= − −− −( ) = −
( ) = − −( ) +
= +
− = bb
b
Y X
X Y
m
b
=
= − +
+ =
=
−( ) = −( ) +
14
34
14
3 4 1
35
2 35
3
9.
10.
11.
−− = − +
− + =
= −
= − − =
2 95
105
95
15
35
15
3 5 1
b
b
b
Y X X Y12.
13.
;
1,, 4, 9, 16, 25, 36, 49, 64, 81,
100, 121, 144, 1169, 196, 225
1 2, , , , , , , ,2 3 4 5 6 7 8 92 2 2 2 2 2 2 22
2 2 2 2 2 210 11 12 13 14 15
804
,
, , , , ,
;
Th14. miles iis and the following
answers may vary, dependingg on
your source of information.
15. 804 50 16 08÷ = .
.
. . min,
hours
hours16 8100
16 08
08 60 4 8
=
× = round tto 5 min
16:05 4:42 20:47 8:47+ ==
;
.
PM
16. 804 25 32÷ 116
32 16 1 289 41 45
368
910
9
. . $ .
.
gallons
( )( ) =
=
17.
18. 00100
90
1 3 3 1 3 3
2
=
−( ) − − −( )−( )
%
; :19. no example
≠
−− − ( )−
× =
3 1 0
5 1
16 24 3 3 888
≠
≠
20. . . .
.
.
. . min,
hours
hours16 8100
16 08
08 60 4 8
=
× = round tto 5 min
16:05 4:42 20:47 8:47+ ==
;
.
PM
16. 804 25 32÷ 116
32 16 1 289 41 45
368
910
9
. . $ .
.
gallons
( )( ) =
=
17.
18. 00100
90
1 3 3 1 3 3
2
=
−( ) − − −( )−( )
%
; :19. no example
≠
−− − ( )−
× =
3 1 0
5 1
16 24 3 3 888
≠
≠
20. . . .
Lesson Practice 15A1. −( )3 2,
Y
X
2.
3.
X Y
X Y
XX
Y
+ = −− + = −
− == −
−( ) + = −
1
2 4
33
3 1
( )
;
YY =− −( )
2
1 14. ,
Y
X
b
a
5.
6.
( )X YX Y
XX
Y
+ = −+ − = −
= −= −
−( ) + = −
23 2
4 41
1 2
,
Y = −−( )
1
4 17.
aLGeBra 1
Lesson Practice 15a - Lesson Practice 15B
soLutions 211
Y
X
8.
9.
X YX Y
XX
Y
− =+ + =
==
( ) − =−
22 7
3 124
4 5
4 5
( )
==− =
+ =( ) => + =− +
Y
Y
X Y X Y
X Y(
1
2 2 3 18 4 6 36
4
10.
====
+ ( ) ===
( )
6
5 306
4 6 6
4 00
0 6
)
,
YY
X
XX
Lesson Practice 15B1. 5 2, ( )
Y
X
a
b
2.
3.
X Y
X Y
XX
− =− − =− = −
=
( )
3
5
3
3 1
2 10
5(( ) − ==
−( )
Y
Y
3
2
2 44. ,
Y
X
5.
6.
3 102 8
2
2 2 84
X YX Y
X
YY
− = −− − = −
= −
−( ) − = −− − = −
( )
884
1 1
Y =( )7. ,
Y
X
8.
( )2 03 2 52 2 0
5 5
X YX YX Y
X
− =( ) =>+ =
+ − ==
XX
YY
X YX Y
X
=
( ) − ==
+ = −+ − = −
= −
1
1 01
33 1
4 4
9.
10.( )
XX
Y Y
= −−( ) + = − => = − − −( )
1
1 3 2 1 2,
aLGeBra 1
Lesson Practice 15B - sYsteMatic reVieW 15c
soLutions212
( )2 03 2 52 2 0
5 5
X YX YX Y
X
− =( ) =>+ =
+ − ==
XX
YY
X YX Y
X
=
( ) − ==
+ = −+ − = −
= −
1
1 01
33 1
4 4
9.
10.( )
XX
Y Y
= −−( ) + = − => = − − −( )
1
1 3 2 1 2,
Systematic Review 15C1.
2.
−( )+ = −
+ − =
2 2
2 3 26 3 18
8
,
( )
see graph
Y XY X
Y
==
( ) − =− =
= −
162
2 2 6
4 6
2
Y
X
X
X
3.
4..
5.
1 1
1 23 2
2
4
,−( )
− − = −( ) =>+ =
− + =
=
see graph
Y XY XY X
X 441
1 21
X
YY
=
− ( ) = −= −
6.
Y
X
(–2,2)
(1,–1)
a b
7.
8.
9.
− > +
< − −
(
2 3 6
32
3
Y X
Y X
on the graph
no see graph))
Y
X
10.
11.
12.
m
b
b
b
Y X
Y
=
( ) = −( ) +
= − +
=
= +
=
12
1 12
1
1 12
32
12
32
2 XX
X Y or X Y
+− = − − + =
3
2 3 2 3
1 4 9 16 25 36 49 64 8, , , , , , , ,13. 11
100 121 144 169 196 225
1 2 3 4 5 62 2 2 2 2
,
, , , , ,
, , , , , 22 2 2
2 2 2 2 2 2 2
7 8
9 10 11 12 13 14 15
6
, , ,
, , , , , ,
14. NN N
N N
N
− =
− ==
( ) − ( ) + − = − + − =
4 102
6 4 5
4
4 2 4 3 4 16 8 12
15.
16. 88 1 9
14 25 3 5
16 8
816
12
3 14 2
+ =× =× =
= =
17.
18.
19.
. .
.
WF
WF
÷ .. .4 1 308
34
56
34
65
1820
910
≈
÷20. = × = =
aLGeBra 1
sYsteMatic reVieW 15D - sYsteMatic reVieW 15e
soLutions 213
Systematic Review 15D1.
2.
3 2
3 2 128 2 10
11
,
( )
see graph( )+ =
+ − ==
Y XY X
Y 222
2
3 2 2 126 2 12
2 63
2 2
Y
XXXX
=( ) + =
+ ===
( )
3.
4. , see graaph
Y
X(2,2)
(3,2)
a
b
c
d
5.
6.
7.
X YX YX
X
Y
Y
Y
+ =− − = −− = −
=( ) + =
=
42 6
2
2
2 4
2
4≥55
2X
o
+
8. n the graph
Y
X
9.
10.
11.
no
m
b
b b
from graph( )= −
( ) = − −( ) += +
2
1 2 1
1 2 ; == −= − −+ = −
1
2 1
2 1
1 4 9 16 25 36 49
12.
13.
Y X
X Y
, , , , , , ,, , ,
, , , , ,
, ,
64 81
100 121 144 169 196 225
1 2 32 2 22 2 2 2 2 2
2 2 2 2 2
4 5 6 7 8
9 10 11 12 13
, , , , , ,
, , , , ,
114 15
3 4 8 3
1 8 38 4
2
3
2 2
2
,
14.
15.
16.
N N N
N NN
N
X
− + =
− + ===
− XX ÷
÷
÷÷
4 3
3 2 2 4 3
3 4 2 112 2 1
12 2 10
2
− =
( ) − ( ) − =( ) − ( ) =
− =− =
177.
18.
19
48100
32 15 36100
15 925
75 5
575
115
× = =
× =
= =
WF
WF
..
20.
21 8 4 54 5
27
12
27
21
47
. . .÷
÷
=
= × =
9.
10.
11.
no
m
b
b b
from graph( )= −
( ) = − −( ) += +
2
1 2 1
1 2 ; == −= − −+ = −
1
2 1
2 1
1 4 9 16 25 36 49
12.
13.
Y X
X Y
, , , , , , ,, , ,
, , , , ,
, ,
64 81
100 121 144 169 196 225
1 2 32 2 22 2 2 2 2 2
2 2 2 2 2
4 5 6 7 8
9 10 11 12 13
, , , , , ,
, , , , ,
114 15
3 4 8 3
1 8 38 4
2
3
2 2
2
,
14.
15.
16.
N N N
N NN
N
X
− + =
− + ===
− XX ÷
÷
÷÷
4 3
3 2 2 4 3
3 4 2 112 2 1
12 2 10
2
− =
( ) − ( ) − =( ) − ( ) =
− =− =
177.
18.
19
48100
32 15 36100
15 925
75 5
575
115
× = =
× =
= =
WF
WF
..
20.
21 8 4 54 5
27
12
27
21
47
. . .÷
÷
=
= × =
Systematic Review 15E1.
2.
1 2
2 2 62 4
2
,−( )− + =+ − = −− =
=
see graph
Y XY XY
Y −−−( ) − = − − = − =−( )
2
2 3 1 1
3 1
3.
4.
X X X; ;
, see graph
aLGeBra 1
sYsteMatic reVieW 15e - Lesson Practice 16a
soLutions214
Y
X
(-3,1)
(1,-2)
a
cb
d
5.
6. ;
X YX YX
X
Y Y
− = −+ + = −
= −= −
−( ) + = − =
2 52 2 43 9
3
3 2 1
77.
8.
9.
Y X
no see
< −
( )
3 4
on the graph
graph
Y
X
10.
11.
12.
m
b
b b
Y X
X Y o
=( ) = ( ) += + = −= −− =
2
1 2 1
1 2 1
2 1
2 1
;
rr X Y
, , , , , , , , ,
− + = −2 1
1 4 9 16 25 36 49 64 81
1
13.
000 121 144 169 196 225
1 2 3 4 52 2 2 2 2
, , , , ,
, , , , ,
6 7 8
9 10 11 12 13 14 15
2 2 2
2 2 2 2 2 2 2
, , ,
, , , , , ,
14..
15.
16.
N N N N
N N
N
X X
− + + = +− = +
= + =
− + =
2 5 6 1
7 2 6 1
1 2 3
5 4 3 2÷
55 3 4 3 3 2
15 4 9 2
11 92
15 12
150100
18
( ) − + ( ) =− + =
+ =
× =
÷
÷
17. 227
95 3 31 67 31 67 2 63 3418. ÷ = × =. ; . .
Using a calculatoor without rounding
the first step will give 63..33.
19.
20.
3 14 4 16 13 06
916
9 16 5625 56
. . .
. .
×
= =
≈
÷ ≈
2 1
1 4 9 16 25 36 49 64 81
1
000 121 144 169 196 225
1 2 3 4 52 2 2 2 2
, , , , ,
, , , , ,
6 7 8
9 10 11 12 13 14 15
2 2 2
2 2 2 2 2 2 2
, , ,
, , , , , ,
14..
15.
16.
N N N N
N N
N
X X
− + + = +− = +
= + =
− + =
2 5 6 1
7 2 6 1
1 2 3
5 4 3 2÷
55 3 4 3 3 2
15 4 9 2
11 92
15 12
150100
18
( ) − + ( ) =− + =
+ =
× =
÷
÷
17. 227
95 3 31 67 31 67 2 63 3418. ÷ = × =. ; . .
Using a calculatoor without rounding
the first step will give 63..33.
19.
20.
3 14 4 16 13 06
916
9 16 5625 56
. . .
. .
×
= =
≈
÷ ≈
Lesson Practice 16A 1.
2.
N D
N D
N D
N D
+ =+ =
+ =( ) −( ) =>+ =
8
05 10 65
8 5
05 10 6
. . .
. . . 55 100
5 5 40
5 10 65
5 25
5
8
( ) =>− − = −
+ ===
+ =+
( )
N D
N D
D
D
N D
N
3.
55 8
3
25
01 10 88
25 10
( ) ==
+ =+ =
+ =( ) −( ) =>
N
P D
P D
P D
4.
5.
. . .
.. . .01 10 88 100
10 10 25010 88
9P D
P DP D
P+ =( )( ) =>
− − = −+ =
− == −=
+ =( ) + =
=
+ =+
162
18
25
18 25
7
26
01 05
P
P D
D
D
P N
P N
6.
7.
. . ==
+ =( ) −( ) =>+ =( )( ) =>
− −
.
. . .
86
26 1
01 05 86 100
8.
P N
P N
P N == −+ =
==
+ =+ ( ) =
=+
26
5 86
4 60
15
26
15 26
11
P N
N
N
P N
P
P
Q
9.
10. DD
Q D
Q D
Q D
=+ =
+ =( ) −( ) =>+ =
13
25 10 1 75
13 10
25 10
. . .
. .
11.
11 75 100
10 10 130
25 10 175
15 45.( )( ) =>
− − = −+ =
==
Q D
Q D
Q
Q 33
13
3 13
10
aLGeBra 1
Lesson Practice 16a - sYsteMatic reVieW 16c
soLutions 215
+ ==
+ =+
162
18
25
18 25
7
26
01 05
P
P D
D
D
P N
P N. . ==
+ =( ) −( ) =>+ =( )( ) =>
− −
.
. . .
86
26 1
01 05 86 100
8.
P N
P N
P N == −+ =
==
+ =+ ( ) =
=+
26
5 86
4 60
15
26
15 26
11
P N
N
N
P N
P
P
Q
9.
10. DD
Q D
Q D
Q D
=+ =
+ =( ) −( ) =>+ =
13
25 10 1 75
13 10
25 10
. . .
. .
11.
11 75 100
10 10 130
25 10 175
15 45.( )( ) =>
− − = −+ =
==
Q D
Q D
Q
Q 33
13
3 13
10
12. Q D
D
D
+ =( ) + =
=
Lesson Practice 16B1.
2.
N D
N D
N D
N
+ =+ =
+ =( ) −( ) =>+
20
05 10 1 75
20 10
05 10
. . .
. . DD
N DN D
N=( )( ) =>
− − = −+ =
− =1 75 100
10 10 2005 10 175
5.
−−=
+ =( ) + =
=+ =
+ =
25
5
20
5 20
15
39
01 10 1
N
N D
D
D
P D
P D
3.
4.
. . .883
39 10
01 10 1 83 100
10
5.
P D
P D
P+ =( ) −( ) =>+ =( )( ) =>
−. . .
−− = −+ =
− = −=
+ =( ) + =
10 39010 183
9 207
23
39
23
DP D
P
P
P D
D
6.
339
16
19
05 10 1 25
19 10
D
N D
N D
N D
=+ =
+ =
+ =( ) −( ) =>
7.
8.
. . .
.005 10 1 25 100
10 10 1905 10 125N D
N DN D+ =( )( ) =>
− − = −+ =
−. .
55 65
13
19
13 19
6
40
25
N
N
N D
D
D
Q N
Q. .
= −=
+ =( ) + =
=+ =
+
9.
10.
005 5 00
40 5
25 05 5 00 100
N
Q N
Q N
=
+ =( ) −( ) =>+ =
.
. . .
11.
=>
− − = −+ =
==
+ =
5 5 200
25 5 500
20 300
15
40
15
Q N
Q N
Q
Q
Q N
−− = −+ =
− = −=
+ =( ) + =
10 39010 183
9 207
23
39
23
DP D
P
P
P D
D
6.
339
16
19
05 10 1 25
19 10
D
N D
N D
N D
=+ =
+ =
+ =( ) −( ) =>
7.
8.
. . .
.005 10 1 25 100
10 10 1905 10 125N D
N DN D+ =( )( ) =>
− − = −+ =
−. .
55 65
13
19
13 19
6
40
25
N
N
N D
D
D
Q N
Q. .
= −=
+ =( ) + =
=+ =
+
9.
10.
005 5 00
40 5
25 05 5 00 100
N
Q N
Q N
=
+ =( ) −( ) =>+ =( )(
.
. . .
11.
)) =>− − = −
+ ===
+ =
5 5 200
25 5 500
20 300
15
40
15
Q N
Q N
Q
Q
Q N12.
(( ) + ==
N
N
40
25
Systematic Review 16C1.
2.
N D
N D
N D
N
+ =+ =
+ =( )( ) =>+
12
05 10 85
05 10 85 100
. . .
. . .
DD
N D
N D
D
D
N D
=( ) −( ) =>+ =
− − = −==
+ =
12 5
5 10 85
5 5 60
5 25
5
13. 22
5 12
7
05 7 10 5 85
35 50 8585 8
N
N
+ ( ) ==
( ) + ( ) =+ =
=
. . .
. . .. . 55
10
01 05 38
01 05 38 100
4.
5.
P N
P N
P N
+ =+ =
+ =( )( ) =>. . .
. . .
PP N
P N
P NP
P
P
+ =( ) −( ) =>+ =
− − = −− = −
=
10 5
5 38
5 5 504 12
3
6. ++ =( ) + =
=
( ) + ( ) =+ =
N
N
N
10
3 10
7
01 3 05 7 38
03 35 38
3
. . .
. . .
. 88 38
2 6 2
3 4 2
2 4 1214
=
− = −( ) −( ) =>− =
− + ==
−
.
7.
8.
Y X
Y X
Y XY
Y 22 6
14 2 620 2
10 10 14
X
XX
X
= −( ) − = −
==
aLGeBra 1
sYsteMatic reVieW 16c - sYsteMatic reVieW 16D
soLutions216
. . .
. . .. . 55
10
01 05 38
01 05 38 100
4.
5.
P N
P N
P N
+ =+ =
+ =( )( ) =>. . .
. . .
PP N
P N
P NP
P
P
+ =( ) −( ) =>+ =
− − = −− = −
=
10 5
5 38
5 5 504 12
3
6. ++ =( ) + =
=
( ) + ( ) =+ =
N
N
N
10
3 10
7
01 3 05 7 38
03 35 38
3
. . .
. . .
. 88 38
2 6 2
3 4 2
2 4 1214
=
− = −( ) −( ) =>− =
− + ==
−
.
7.
8.
Y X
Y X
Y XY
Y 22 6
14 2 620 2
10 10 14
X
XX
X
= −( ) − = −
== ( ); ,
Y
X
#11
#9
#10
9.
10.
m
b b
Y X
= − −− −
= −−
=
( ) = ( ) + => == +
−( ) =
2 53 4
77
1
5 1 4 1
1
2 1112 1
3
3 3 3
2
( ) +− = +
= −= − − = − + = −
−
bb
b
Y X or X Y or X Y
11. (( ) = − ( ) +− = − + => = −= − −
11
2 1 1
1
b
b b
Y X
12. Since the probllem uses both
inches and feet, we will convert
the original length of the vine to
feet, to maake the units consistent.
24" = = + =2 2 2'; Y X or L 22 2
2 3 2
6 2 8
3
W
Y
Y
new Y X
( ) += ( ) += + =
=
13.
14.
'
equation: ++= ( ) += + =
+( ) × −( ) − − = ( ) × −
2
3 9 2
27 2 29
3 5 2 7 3 3 8 52
Y
Y '
15. (( ) − −= − − − = −
= ×
3 9
40 3 9 52
4
13 13 12
16.
17.
18.
19.
th
no
yes
33 169
64 8
=
=20.
Since the probllem uses both
inches and feet, we will convert
the original length of the vine to
feet, to maake the units consistent.
24" = = + =2 2 2'; Y X or L 22 2
2 3 2
6 2 8
3
W
Y
Y
new Y X
( ) += ( ) += + =
=
13.
14.
'
equation: ++= ( ) += + =
+( ) × −( ) − − = ( ) × −
2
3 9 2
27 2 29
3 5 2 7 3 3 8 52
Y
Y '
15. (( ) − −= − − − = −
= ×
3 9
40 3 9 52
4
13 13 12
16.
17.
18.
19.
th
no
yes
33 169
64 8
=
=20.
Systematic Review 16D1.
2.
N D
N D
N D
N D
+ =+ =
+ =( )( ) =>+
9
05 10 60
05 10 60 100
. . .
. . .
==( ) −( ) =>+ =
− − = −==
+ =+
9 5
5 10 60
5 5 45
5 15
3
9
N D
N D
D
D
N D
N
3.
33 9
6
05 6 10 3 60
30 30 6060 60
( ) ==
( ) + ( ) =+ =
=
N
P
. . .
. . .. .
4. ++ =+ =
+ =( )( ) =>+ =
N
P N
P N
P N
6
01 05 26
01 05 26 100
6
. . .
. . .5.(( ) −( ) =>
+ =− − = −− = −
=
+ =( ) +
5
5 26
5 5 304 4
1
6
1
P N
P NP
P
P N
N
6.
===
+ = −− = −
= −= −
−( ) − = −−
65
4 3 193 1
5 20
4
4 3 1
N
Y XY X
Y
Y
X
7.
8.33 3
1
53
1 53
1
1 5
XX
m
b
== −
= − ( )
−( ) = − ( ) +
− = −
9. from graph
3323
53
23
5 3 2
+
=
= − + + =
b
b
Y X or X Y
aLGeBra 1
sYsteMatic reVieW 16D - sYsteMatic reVieW 16e
soLutions 217
===
+ = −− = −
= −= −
−( ) − = −−
65
4 3 193 1
5 20
4
4 3 1
N
Y XY X
Y
Y
X
7.
8.33 3
1
53
1 53
1
1 5
XX
m
b
== −
= − ( )
−( ) = − ( ) +
− = −
9. from graph
3323
53
23
5 3 2
+
=
= − + + =
b
b
Y X or X Y
Y
X#11
#10
#9 (a)
10. 2 53
2
2 103
163
53
163
5 3
( ) = − ( ) +
= − +
=
= − + +
b
b
b
Y X or X Y ==
−( ) = −( ) +
− = − +
= −
= −
16
6 35
2
6 65245
35
245
11. b
b
b
Y X or 33 5 243 5 24
2 4
8
X Yor X Y
Y X
Y X
Y X
− =− + = −
= += +
= +
12.
13.
14.
88 12 4
8
0 4
4
8
4 8
( ) −( ) =>= +
− = − −= −=
= += ( ) +
Y XY X
X
X
Y X
YY
15.
==
= ( ) += + == += ( ) +
12
2 12 424 4 28
8
12 8
16. YYY X
Y
$ for Kim
==
− −( ) + −( ) =
− −( ) + −( ) =−
$20
5 9 14 17
4 3
2 2
2 2
for Ali
17.
116 9 7
3
+ = −18.
19.
20.
rd
no
yes
b
b
b
Y X or 33 5 243 5 24
2 4
8
X Yor X Y
Y X
Y X
Y X
− =− + = −
= += +
= +88 1
2 48
0 4
4
8
4 8
( ) −( ) =>= +
− = − −= −=
= += ( ) +
Y XY X
X
X
Y X
YY
15.
==
= ( ) += + == += ( ) +
12
2 12 424 4 28
8
12 8
16. YYY X
Y
$ for Kim
==
− −( ) + −( ) =
− −( ) + −( ) =−
$20
5 9 14 17
4 3
2 2
2 2
for Ali
17.
116 9 7
3
+ = −18.
19.
20.
rd
no
yes
Systematic Review 16E1.
2.
N D
N D
N D
+ =+ =
+ =( )( ) =>
14
05 10 1 10
05 10 1 10 100
. . .
. . .
NN D
N DN D
D
D
N
+ =( ) −( ) =>+ =
− − = −==
+
14 5
5 10 1105 5 70
5 40
8
3. DD
N
N
=+ ( ) =
=
( ) + ( ) =+ =
14
8 14
6
05 6 10 8 1 10
30 80 1 10
1
. . .
. . .
.. .
. . .
. . .
10 1 10
8
01 05 20
01 05 20 1
=+ =
+ =
+ =( )
4.
5.
P N
P N
P N 000
8 5
5 20
5 5 404 20
5
( ) =>+ =( ) −( ) =>
+ =− − = −
− = −=
P N
P N
P NP
P
66. P N
N
N
+ =( ) + =
=
( ) + ( ) =+ =
8
5 8
3
01 5 05 3 20
05 15 20
. . .
. . ..220 20
2 2
4 4
== += − −
.
7. Y X
Y X
replace Y in equation 1
witth its equivalent, − −( )− −( ) = +
− ==
4 4
4 4 2 26 6
X
X XXX
:
−−1
8. replace X in equation 1
with its equivalent,,
on the graph
−( )= −( ) += − + =
1
2 1 2
2 2 0
:
Y
Y
9.
aLGeBra 1
sYsteMatic reVieW 16e - Lesson Practice 17a
soLutions218
66. P N
N
N
+ =( ) + =
=
( ) + ( ) =+ =
8
5 8
3
01 5 05 3 20
05 15 20
. . .
. . ..220 20
2 2
4 4
== += − −
.
7. Y X
Y X
replace Y in equation 1
witth its equivalent, − −( )− −( ) = +
− ==
4 4
4 4 2 26 6
X
X XXX
:
−−1
8. replace X in equation 1
with its equivalent,,
on the graph
−( )= −( ) += − + =
1
2 1 2
2 2 0
:
Y
Y
9.
Y
X
#11
#10 #9
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
0 3 0 b
0 0 b; b 0
Y 3X or 3X Y 0
m 13
Y 13
X or X 3Y 0 or X 3Y 0
T 5M 100
T 5 15 100 175ºC
T 10M 100
T 10 15 100
T 150 100 250ºC
7 5 3 8
7 5 5
12 25
144 25 119
2nd
yes
no
25 25 25 625
225 15
2 2
2 2
2
2
[ ][ ]
( ) ( )
( )
( )
( ) ( )( )( )
= − += + == − + =
=
= − = − + =
= += + == += += + =
− − − + − =
− + + − =
− + =− + = −
= × =
=
Lesson Practice 17A1.
2.
3.
N N N
N N N N
N N
; ;+ ++ +( ) + +( ) + = +( )+ +( ) +
1 2
1 2 4 4 1
1 NN NN N
N NN
+( ) + = +( )+ = +− = −
=
+
2 4 4 13 7 4 4
7 4 4 33
3 4 5
3
; ;
4. 44 5 4 4 4
16 16
2 4
2 4
( ) + ( ) + = ( )=
+ ++ +( ) = +(
5.
6.
N N N
N N N
; ;)) +
+ +( ) = +( ) ++ = +− = −
=
4
2 4 42 2 82 8 2
6
6 8 1
7. N N NN NN N
N
; ; 00
6 8 10 4
14 14
1 2
5 1 3
8.
9.
10.
( ) + ( ) = ( ) +=
+ +
+( ) =N N N
N
; ;
NN N
N N N
N N
+ +( ) +
+( ) = + +( ) ++ = +
2 2
5 1 3 2 2
5 5 3 2
11.
22 2
5 5 6 6 25 5 6 8
5 8 6 53
3 2
[ ] ++ = + ++ = +− = −− =
− −
N NN N
N NN
; ; −−
−( ) = −( ) + −( ) +− = −[ ] +− = −[
1
5 2 3 3 1 2
10 3 4 2
10 3 4
12.
]] +− = − +− = −
+ ++ +( ) =
2
10 12 210 10
2 4
4 3
13.
14.
N N N
N N N
; ;
++( ) ++ +( ) = +( ) +
+ = + ++ = +
2 3
4 3 2 32 4 3 6 32 4 3 9
4
15. N N NN NN N−− = −− =
− − −
−( ) + −( ) = −( ) +− = −
9 3 25
5 3 1
5 1 3 3 3
6
N NN
; ;
16.
66
aLGeBra 1
Lesson Practice 17B - sYsteMatic reVieW 17c
soLutions 219
Lesson Practice 17B1.
2.
3.
N N N
N N N
N N N
; ;+ +
+( ) = + +( )( ) ++( ) = +
2 4
3 4 2 2 2
3 4 2 ++( )( ) ++ = +( ) ++ = + ++ = +
2 2
3 12 2 2 2 23 12 4 4 23 12 4 61
N NN NN N22 6 4 3
6
6 8 10
3 10 2 6 8 2
30 2 14
− = −=
( ) = ( ) + ( )( ) +=
N NN
; ;
4.
(( ) += +=
+ ++ +( ) = +( )
230 28 230 30
1 2
2 20 1
5.
6.
N N N
N N N
; ;
77. N N NN N
N NN
+ +( ) = +( )+ = +
− = −− =
2 20 12 2 20 20
2 20 20 218 18
−− =−
−( ) + ( ) = ( )=
+ +
1
1 0 1
1 1 20 0
0 0
1 2
N
N N N
; ;
; ;
8.
9.
10..
11.
5 2 1 6 2
5 2 1 6 25 2
N N N
N N NN N
( ) + +( ) = +( )( ) + +( ) = +( )
+ +22 6 127 2 6 12
7 6 12 210
10 11 12
5 1
= ++ = +
− = −=
NN N
N NN
; ;
12. 00 2 11 6 12
50 22 72
72 72
2 4
( ) + ( ) = ( )+ =
=+ +13.
14.
N N N
N
; ;
++ +( ) = +( ) ++ +( ) = +( ) +
+ = + +
N N
N N NN N
4 3 2 19
4 3 2 192 4 3 6
15.119
2 3 25 42121
21 19 17
21 1
N NNN
− = −− =
= −
− − −
−( ) + −
; ;
16. 77 3 19 19
38 57 19
38 38
( ) = −( ) +− = − +− = −
+
+ +( ) = +( ) ++ = + +
N N
N N NN N
4 3 2 19
4 3 2 192 4 3 6
15.119
2 3 25 42121
21 19 17
21 1
N NNN
− = −− =
= −
− − −
−( ) + −
; ;
16. 77 3 19 19
38 57 19
38 38
( ) = −( ) +− = − +− = −
Systematic Review 17C1.
2.
3.
N N N
N N N
N N
; ;+ ++( ) − ( ) = +( )+( ) − ( ) =
2 4
5 4 4 4 2
5 4 4 44 25 20 4 4 85 4 4 8 20
3 124
4 6
NN N NN N N
NN
+( )+ − = +− − = −
− = −=
; ;;
; ;
8
1 2
6 1 4 9 2 4
6 1
4.
5.
6.
N N N
N N N
N
+ ++( ) + ( ) = +( ) −+( ) ++ ( ) = +( ) −+ + = + −
+ − = − −=
4 9 2 46 6 4 9 18 4
6 4 9 18 4 6
N NN N N
N N NN 88
8 9 10
11
05 10 80
05 10 80 1
; ;
. . .
. . .
7. N D
N D
N D
+ =+ =
+ =( ) 000
11 5
5 10 80
5 5 55
5 25
( ) =>+ =( ) −( ) =>
+ =− − = −
==
N D
N D
N D
DD 55
11 5 11
6
05 6 10 5 80
30 50
N D N
N
+ = => + ( ) ==
( ) + ( ) =+ =
. . .
. . .88080 80
4 4
5 4 9 4 4
. .
;
=> −− > − => > −
8.
9.
Y X
Y X Y X on graph
1.
2.
3.
N N N
N N N
N N
; ;+ ++( ) − ( ) = +( )+( ) − ( ) =
2 4
5 4 4 4 2
5 4 4 44 25 20 4 4 85 4 4 8 20
3 124
4 6
NN N NN N N
NN
+( )+ − = +− − = −
− = −=
; ;;
; ;
8
1 2
6 1 4 9 2 4
6 1
4.
5.
6.
N N N
N N N
N
+ ++( ) + ( ) = +( ) −+( ) ++ ( ) = +( ) −+ + = + −
+ − = − −=
4 9 2 46 6 4 9 18 4
6 4 9 18 4 6
N NN N N
N N NN 88
8 9 10
11
05 10 80
05 10 80 1
; ;
. . .
. . .
7. N D
N D
N D
+ =+ =
+ =( ) 000
11 5
5 10 80
5 5 55
5 25
( ) =>+ =( ) −( ) =>
+ =− − = −
==
N D
N D
N D
DD 55
11 5 11
6
05 6 10 5 80
30 50
N D N
N
+ = => + ( ) ==
( ) + ( ) =+ =
. . .
. . .88080 80
4 4
5 4 9 4 4
. .
;
=> −− > − => > −
8.
9.
Y X
Y X Y X on graph
Y
X
aLGeBra 1
sYsteMatic reVieW 17c - sYsteMatic reVieW 17D
soLutions220
10.
11.
yes
Y X
Y X
Y XX
X
2 3 9 24 11
4 6 187 7
− =( ) −( ) =>+ =
− + = −= −== −
+ = => + −( ) ===
+ =
=
1
4 11 4 1 114 12
3
4 11
Y X YYY
Y X
Y
12.
−− +
( ) = − ( ) +=
= − + + =
14
114
1 14
0
1
14
1 4 4
21
X
b
b
Y X or X Y
13.
114.
15.
16.
4 2 23
4 8 234 23 8
3 155
N N
N NN N
NN
+( ) = +
+ = +− = −
==
22 3 1
2 5 3 1 5
2 2 1 5
X X−( ) + =( ) −( ) + ( ) =
( ) +
÷
÷
÷ ==+[ ] =
=
+ = + = =
× =
4 1 5
5 5 1
12
23
36
46
76
1 16
75 250
÷
÷
17.
18. . 1187 5
1 8 16 10
100 1 8 100 16 100 10
1
.
. .
. .
19. − =( ) − ( ) = ( )
A
A
880 16 100016 820
82016
51 14
51 25
− =− =
=−
= − −
AA
A or .
20. 22 2 2 2 2 3× × × × ×
10.
11.
yes
Y X
Y X
Y XX
X
2 3 9 2
4 11
4 6 187 7
− =( ) −( ) =>+ =
− + = −= −== −
+ = => + −( ) ===
+ =
=
1
4 11 4 1 114 12
3
4 11
Y X YYY
Y X
Y
12.
−− +
( ) = − ( ) +=
= − + + =
14
114
1 14
0
1
14
1 4 4
21
X
b
b
Y X or X Y
13.
114.
15.
16.
4 2 23
4 8 234 23 8
3 155
N N
N NN N
NN
+( ) = +
+ = +− = −
==
22 3 1
2 5 3 1 5
2 2 1 5
X X−( ) + =( ) −( ) + ( ) =
( ) +
÷
÷
÷ ==+[ ] =
=
+ = + = =
× =
4 1 5
5 5 1
12
23
36
46
76
1 16
75 250
÷
÷
17.
18. . 1187 5
1 8 16 10
100 1 8 100 16 100 10
1
.
. .
. .
19. − =( ) − ( ) = ( )
A
A
880 16 100016 820
82016
51 14
51 25
− =− =
=−
= − −
AA
A or .
20. 22 2 2 2 2 3× × × × ×
Systematic Review 17D1.
2.
3.
N N N
N N N
N
; ;+ ++( ) + = ( ) + +( )+( ) + =
2 4
4 4 1 3 2 2
4 4 1 3 NN NN N N
N N NN
( ) + +( )+ + = + +
− = + −=
2 24 16 1 3 2 4
17 4 3 2 413
13; 115 17
1 2
3 5 1 1
3 5 1
;
; ;4.
5.
6.
N N N
N N
N N
+ +( ) − +( ) = −( ) − +(( ) = −
− − = −− = − +− =
= −− −
+
13 5 5 1
2 1 52 4
2
2 1 0
N NNNN
N D
; ;
1.
2.
3.
N N N
N N N
N
; ;+ ++( ) + = ( ) + +( )+( ) + =
2 4
4 4 1 3 2 2
4 4 1 3 NN NN N N
N N NN
( ) + +( )+ + = + +
− = + −=
2 24 16 1 3 2 4
17 4 3 2 413
13; 115 17
1 2
3 5 1 1
3 5 1
;
; ;4.
5.
6.
N N N
N N
N N
+ +( ) − +( ) = −( ) − +(( ) = −
− − = −− = − +− =
= −− −
+
13 5 5 1
2 1 52 4
2
2 1 0
N NNNN
N D
; ;
7. ==+ =
+ =( )( ) =>+ =
15
05 10 1 10
05 10 1 10 100
15
. . .
. . .
N D
N D
N D(( ) −( ) =>+ =
− − = −==
+ = => +
5
5 10 1105 5 75
5 35
7
15
N DN D
D
D
N D N 77 158
05 8 10 7 1 10
40 70 1 10
1 10 1
( ) ==
( ) + ( ) =+ =
=
N
. . .
. . .
. .110
28.
9.
10.
Y X
see
yes
> − graph
Y
X
aLGeBra 1
sYsteMatic reVieW 17D - sYsteMatic reVieW 17e
soLutions 221
11.
5 3 22 1
5 6 195 3 22
3 3
1
5
Y X
Y XY X
X
X
Y
+ = −( ) −( ) =>+ = −
− − ===
++ = − => + ( ) = −+ = −
= −= −
−( )
6 19 5 6 1 195 6 19
5 25
5
1 5
X YY
Y
Y
,
122. 5 6 19 65
195
1 56
4
1 206
2
Y X Y X
b
b
b
+ = − => = − −
( ) = −( ) +
= − +
= 666
133
56
133
6 265 6 26
6
=
= + − = −− + =
=
Y X or X Yor X Y
5
13. 22 3 8 2 2 2 2 2 2 3 24
2 6 8 4
2
× = × × = × × × =− + =
−
; ; LCM
14.
15.
N N
N 66 8 410 10
1
3 13 4
3 1 1 13 4 1
2
2
+ ===
− + − =
( ) − ( ) + − (
NNN
X X X16.
)) =− + − =
+ = + =
× =
3 1 13 4 11
16
34
212
912
1112
13 180 2
17.
18. . 33 4
6 16 4 206 4 20 16
2 3618
3 3 3
.
19.
20.
A AA A
AA
− − =− = +
==
× × ×55
11.
5 3 22 1
5 6 195 3 22
3 3
1
5
Y X
Y XY X
X
X
Y
+ = −( ) −( ) =>+ = −
− − ===
++ = − => + ( ) = −+ = −
= −= −
−( )
6 19 5 6 1 195 6 19
5 25
5
1 5
X YY
Y
Y
,
122. 5 6 19 65
195
1 56
4
1 206
2
Y X Y X
b
b
b
+ = − => = − −
( ) = −( ) +
= − +
= 666
133
56
133
6 265 6 26
6
=
= + − = −− + =
=
Y X or X Yor X Y
5
13. 22 3 8 2 2 2 2 2 2 3 24
2 6 8 4
2
× = × × = × × × =− + =
−
; ; LCM
14.
15.
N N
N 66 8 410 10
1
3 13 4
3 1 1 13 4 1
2
2
+ ===
− + − =
( ) − ( ) + − (
NNN
X X X16.
)) =− + − =
+ = + =
× =
3 1 13 4 11
16
34
212
912
1112
13 180 2
17.
18. . 33 4
6 16 4 206 4 20 16
2 3618
3 3 3
.
19.
20.
A AA A
AA
− − =− = +
==
× × ×55
Systematic Review 17E 1.
2.
3.
N N N
N N N
N N
; ;+ +( ) + +( ) = +( ) +( ) + +
2 4
5 3 4 7 2 10
5 3 4(( ) = +( ) ++ + = + ++ − = + −
7 2 105 3 12 7 14 10
5 3 7 14 10 12
NN N N
N N NNN
N N N
N N N
=
+ ++( ) − +( ) = (
12
12 14 16
1 2
7 2 5 1 4
; ;
; ;4.
5. )) ++( ) − +( ) = ( ) ++ − − = +
− −
1
7 2 5 1 4 17 14 5 5 4 1
14 5 1
6. N N NN N N
== − +==
+ =+ =
4 7 58 2
4
4 5 6
7
10 25 1 00
1
N N NN
N
D Q
D Q
; ;
. . .
.
1.
2.
3.
N N N
N N N
N N
; ;+ +( ) + +( ) = +( ) +( ) + +
2 4
5 3 4 7 2 10
5 3 4(( ) = +( ) ++ + = + ++ − = + −
7 2 105 3 12 7 14 10
5 3 7 14 10 12
NN N N
N N NNN
N N N
N N N
=
+ ++( ) − +( ) = (
12
12 14 16
1 2
7 2 5 1 4
; ;
; ;4.
5. )) ++( ) − +( ) = ( ) ++ − − = +
− −
1
7 2 5 1 4 17 14 5 5 4 1
14 5 1
6. N N NN N N
== − +==
+ =+ =
4 7 58 2
4
4 5 6
7
10 25 1 00
1
N N NN
N
D Q
D Q
; ;
. . .
.
7.
00 25 1 00 100
7 10
10 25 100D Q
D Q
D Q+ =( )( ) =>+ =( ) −( ) =>
+ =. .
−− − = −==
+ = => + ( ) = => =( )
10 10 70
15 30
2
7 2 7 5
10 5
D Q
Q
Q
D Q D D
. ++ ( ) =+ =
=− +
. .
. . .. .
25 2 1 00
50 50 1 001 00 1 00
2 48.
9.
Y X≥
on graph
10. yes
Y
X
11. Y X Y X+ = => = −0
replace Y in equation 1
with its eqquivalent, −( )−( ) − = −
− = −= −( )
X
X XX
X
Y
:
,
3 44 4
1 1 1
12. −− = − => = −
−( ) = ( ) +− = +
= −= −
3 4 3 4
2 3 22 6
8
3 8 3
X Y X
bb
b
Y X or XX Y or X Y
s multiples
− = − + = −8 3 8
15 15 30 45' : , ,13. ,, , ,
' : , , , ,
60 75 90
25 25 50 75 100 1s multiples 225
2 1 8 18
first match, or LCM, is 75
14. + −( ) = −22
2 1 8 18 2
2 7 18 2
14 18 214
N
N
N
N
15. + −( ) = −−
aLGeBra 1
sYsteMatic reVieW 17e - sYsteMatic reVieW 18c
soLutions222
11. Y X Y X+ = => = −0
replace Y in equation 1
with its eqquivalent, −( )−( ) − = −
− = −= −( )
X
X XX
X
Y
:
,
3 44 4
1 1 1
12. −− = − => = −
−( ) = ( ) +− = +
= −= −
3 4 3 4
2 3 22 6
8
3 8 3
X Y X
bb
b
Y X or XX Y or X Y
s multiples
− = − + = −8 3 8
15 15 30 45' : , ,13. ,, , ,
' : , , , ,
60 75 90
25 25 50 75 100 1s multiples 225
2 1 8 18
first match, or LCM, is 75
14. + −( ) = −22
2 1 8 18 2
2 7 18 2
14 18 214
N
N
N
N
15. + −( ) = −−[ ] = −− = −
− −118 232 216
3 5 6 10 6
3 16 5 6 1
= −− = −
=− + + −( ) =>
( ) − +
NN
N
Y Y16.
66 10 6
48 5 96 4 143
27
114
414
114
314
( ) + −( ) =− + + =
− = − =17.
188.
19.
1 20 100 120
5 1 5 4 5
10 5 10 1 5 10
.
. . .
. .
× =
+ =( ) + ( ) =
X
X 44 5
5 15 45
5 306
2 3 17
.( )+ =
==
× ×
X
XX
20.
Lesson Practice 18A1.
2.
3.
4.
15 15 15 225
169 13
8 8 8 64
10
2
2
= × =
=
−( ) = −( ) −( ) =− 00 10
16 16 16 256
144 12
4 4 4 4
8
2
5 2 5 2 7
= −
= × =
=
⋅ = =+
5.
6.
7.
8. 44 7 4 7 11
7 3 7 3 4
8 4 8 4 12
8 8 8
8 8 8 8
3 3 3 3
⋅ = =
= =
⋅ = =
+
−
+
9.
10.
1
÷
11.
12.
B B B B B
CD D C D C D C
2 3 5 2 3 5 10
1 5 4 3 2 1 3 5 4 2 4
= =
= =
+ +
+ + + DD
M M M M
X Y X Y
X X X X X
11
10 3 10 3 7
9
8 8 8
8 8
13.
14.
15.
⋅ =
= =
⋅
+
−÷110 3 9 10 3 16
5 2 5 2 3
8 8 8÷
÷
= =
= =
+ −
−16. X X X XY Y Y Y Y
00 10
16 16 16 256
144 12
4 4 4 4
8
5.
6.
7.
8. 44 7 4 7 11
7 3 7 3 4
8 4 8 4 12
8 8 8
8 8 8 8
3 3 3 3
⋅ = =
= =
⋅ = =
+
−
+
9.
10.
1
÷
11.
12.
B B B B B
CD D C D C D C
2 3 5 2 3 5 10
1 5 4 3 2 1 3 5 4 2 4
= =
= =
+ +
+ + + DD
M M M M
X Y X Y
X X X X X
11
10 3 10 3 7
9
8 8 8
8 8
13.
14.
15.
⋅ =
= =
⋅
+
−÷110 3 9 10 3 16
5 2 5 2 3
8 8 8÷
÷
= =
= =
+ −
−16. X X X XY Y Y Y Y
Lesson Practice 18B1.
2.
3.
4
25 25 25 625
2 2 2 2 8
9 9 9 81
2
3
2
= × =
= × × =
−( ) = −( ) −( ) =..
5.
6.
7 7 7 7 343
17 17 17 289
81 9
3
2
( ) = × × =
−( ) = −( ) −( ) =− = −
77.
8.
9.
5 5 5 5
6 6 6 6
18 18 18
3 6 3 6 9
4 2 4 2 6
13 9 13
⋅ = =
⋅ = =
=
+
+
−÷ 99 4
8 5 8 5 13
2
1 2
18
4 4 4 4
4 4 4 16
=
⋅ = =( ) = ×( ) =
+10.
11.
12. C C C33 1 2 3 6
3 4 5 2 5 3 4 2 5 9
6 1 3
= =
= =
+ +
+ +
C C
F F E F E F E F
B C C B
13.
14. 77 6 7 1 3 13 4
10 5 3 10 5 3 12
8
= =
⋅ = =
+ +
+ −
B C B C
Y Y Y Y Y
A X
15.
16.
÷
÷÷ A A AX X X X3 8 3 5= =−
Systematic Review 18CSystematicReview17C1.
2.
3.
14 14 14 196
121 11
2 = × =
=
−99 9 9 81
49 7
3 3 3 3
5 5
2
3 3 3 3 6
2 6
( ) = −( ) −( ) =− = −
⋅ = =
⋅
+
4.
5.
6. == =
= =
⋅ = =
+
−
+
5 5
6 6 6 6
4 4 4 4
2 6 8
5 2 5 2 3
5 2 5 2 7
5 2 4
7.
8.
9.
÷
A A B BB A B A B
B B B B
A A A
Y Y Y Y Y
1 5 2 4 1 7 5
2 2 3
5 1 5
= =
⋅ = =
=
+ +
+10.
11. ÷ −−
+ −
=
⋅ = =
1 4
5 2 7 5 2 7 0 1
A
X X X X X or
add
subtra
12.
13.
14.
÷
cct
N N N
N N N
15.
16.
5 2 2 4 1 40
5 2 2 4 1
+( ) − ( ) = +( ) −+( ) − ( ) = +( )) −+ − = + −− − = − −
− = −=
405 10 2 4 4 40
5 2 4 4 40 1046
46
N N N
N N NNN
446 47 48
20
05 10 1 60
05 10 1
; ;
. . .
. . .
aLGeBra 1
sYsteMatic reVieW 18c - sYsteMatic reVieW 18e
soLutions 223
== =
= =
⋅ = =
+
−
+
5 5
6 6 6 6
4 4 4 4
2 6 8
5 2 5 2 3
5 2 5 2 7
5 2 4
7.
8.
9.
÷
A A B BB A B A B
B B B B
A A A
Y Y Y Y Y
1 5 2 4 1 7 5
2 2 3
5 1 5
= =
⋅ = =
=
+ +
+10.
11. ÷ −−
+ −
=
⋅ = =
1 4
5 2 7 5 2 7 0 1
A
X X X X X or
add
subtra
12.
13.
14.
÷
cct
N N N
N N N
15.
16.
5 2 2 4 1 40
5 2 2 4 1
+( ) − ( ) = +( ) −+( ) − ( ) = +( )) −+ − = + −− − = − −
− = −=
405 10 2 4 4 40
5 2 4 4 40 1046
46
N N N
N N NNN
446 47 48
20
05 10 1 60
05 10 1
; ;
. . .
. . .
17. N D
N D
N D
+ =+ =
+ = 660 100
20 5
5 10 160
5 5 100
( )( ) =>+ =( ) −( ) =>
+ =− − = −N D
N D
N D
55 60
12
20 12 208
6 3 10
3 6
D
D
N D NN
X Y
Y X
==
+ = => + ( ) ==
+ == −
18.
++
= − +
= += +
= + => +( ) = +
10
2 103
3 2
4
4 4 3 2
Y X
Y X
Y X
Y X X X
19.
20.44 2 3
2 21
4 1 45
− = −==
= + => = ( ) +=
X XX
X
Y X YY
In 1 year, theyy will have an equal
height of 5 feet.
Systematic Review 18D1.
2.
3.
− = − ×( ) = −
− = −
−( ) = −( ) −
13 13 13 169
144 12
15 15 1
2
255 225
100 10
7 7 7 7 7
2 2 2 2
3 4 3 4 1 8
8 3 2
( ) ==
⋅ ⋅ = =
⋅ ⋅ =
+ +
4.
5.
6. 88 3 2 13
2 9 2 9 11
4 5 2 4 5 2 9 2
2+ +
+
+
=
⋅ = =
= =
7.
8.
9
X X X X
A A B A B A B
..
10.
11.
8 8 8 8
10 10 10 10
5 3 5 3 2
5 5 1 4
10 4 10
÷
÷
÷
= =
= =
=
−
−
X X X −−
+ −
=
⋅ = =
4 6
4 3 4 3 6
X
X X X X X
divide
mul
Y Y Y Y Y Y Y12.
13.
14.
÷
ttiply
N N N
N N
15.
16.
4 2 3 4 8 11
4 2 3 4
+( ) + +( ) = ( ) −+
1.
2.
3.
= −
− = −
−( ) = −( ) −
13 13 13 169
144 12
15 15 155 225
100 10
7 7 7 7 7
2 2 2 2
3 4 3 4 1 8
8 3 2
( ) ==
⋅ ⋅ = =
⋅ ⋅ =
+ +
4.
5.
6. 88 3 2 13
2 9 2 9 11
4 5 2 4 5 2 9 2
2+ +
+
+
=
⋅ = =
= =
7.
8.
9
X X X X
A A B A B A B
..
10.
11.
8 8 8 8
10 10 10 10
5 3 5 3 2
5 5 1 4
10 4 10
÷
÷
÷
= =
= =
=
−
−
X X X −−
+ −
=
⋅ = =
4 6
4 3 4 3 6
X
X X X X X
divide
mul
Y Y Y Y Y Y Y12.
13.
14.
÷
ttiply
N N N
N N
15.
16.
4 2 3 4 8 11
4 2 3 4
+( ) + +( ) = ( ) −+( ) + +( ) = 88 11
4 8 3 12 8 118 12 11 8 4 3
31
31
NN N N
N N NN
( ) −+ + + = −
+ + = − −=
, ,
. . .
. . .
33 35
7
25 10 1 60
25 10 1 60 1
17. Q D
Q D
Q D
+ =+ =
+ =( ) 000
7 10
25 10 160
10 10 70
15
( ) =>+ =( ) −( ) =>
+ =− − = −Q D
Q D
Q D
Q ===
+ = => ( ) + ==
= +
90
6
7 6 7
1
37 30
Q
Q D D
D
Y X18.
19..
20.
215 37 30
185 37
18537
5
326 37
( ) = +=
= =
( ) =
X
X
X weeks
XX
X
X weeks
+=
= =
30
296 37
29637
8
Systematic Review 18E1.
2.
3.
4.
− = − ×( ) = −
=
= × =
− = −
11 11 11 121
196 14
7 7 7 49
225
2
2
115
5 5 5 5
2 4 2 4 6
3 4 3 4 7
2 3 6 1 2
5.
6.
7.
A A A A
A B B A C A
⋅ = =
⋅ = =
=
+
+
22 1 3 6 2 3 9 2
4 3 4 3 1
9 3 9 39 9 9
+ +
−
−
=
= = =
= =
B C A B C
X X X X X8.
9.
÷
÷ 99
11 11 11 11
6
4 6 4 6 10
3 2 3 2
10.
11.
12.
⋅ = =
÷ = =
+
−D D D DX X X X X
MM M M M M
same base
N
5 3 3 5 3 3 5
10 10
4
⋅ = =−
+
+ −÷
13.
14.
15.
,
22 3 3 4
4 2 3 3 44 8 3 3
( ) = ( ) + +( )+( ) = ( ) + +( )+ = +
N N
N N NN N N
16.++
− = + −− =− = −
+ =
128 12 3 3 4
4 22 2 0 2
10
25
N N NN
N
Q D
Q
; ;
.
aLGeBra 1
sYsteMatic reVieW 18e - Lesson Practice 19B
soLutions224
= −
=
= × =
− = −
11 11 11 121
196 14
7 7 7 49
225 115
5 5 5 5
2 4 2 4 6
3 4 3 4 7
2 3 6 1 2
5.
6.
7.
A A A A
A B B A C A
⋅ = =
⋅ = =
=
+
+
22 1 3 6 2 3 9 2
4 3 4 3 1
9 3 9 39 9 9
+ +
−
−
=
= = =
= =
B C A B C
X X X X X8.
9.
÷
÷ 99
11 11 11 11
6
4 6 4 6 10
3 2 3 2
10.
11.
12.
⋅ = =
÷ = =
+
−D D D DX X X X X
MM M M M M
same base
N
5 3 3 5 3 3 5
10 10
4
⋅ = =−
+
+ −÷
13.
14.
15.
,
22 3 3 4
4 2 3 3 44 8 3 3
( ) = ( ) + +( )+( ) = ( ) + +( )+ = +
N N
N N NN N N
16.++
− = + −− =− = −
+ =
128 12 3 3 4
4 22 2 0 2
10
25
N N NN
N
Q D
Q
; ;
.
17.
++ =
+ =( )( ) =>+ =( ) −( )
. .
. . .
10 1 75
25 10 1 75 100
10 10
D
Q D
Q D ==>
+ =− − = −
==
+ = =
25 10 175
10 10 100
15 75
5
10
Q D
Q D
Q
Q
Q D >> ( ) + ==
+ == += +
5 10
5
4 16
25 50
10 200
D
D
X Y
Y X
Y X
Y
18.
19.
20. == + => +( ) = +− = −
=
10 200 25 50 10 200
25 10 200 5015 15
X X X
X XX 00
10
10 200 10 10 200
100 2003
X hours
Y X Y
YY
=
= + => = ( ) += += 000 gizmos
Lesson Practice 19A1.
2.
3.
4.
5.
6.
1
44
1
77
1
44
1
33
5 1
5
22
22
33
22
33
=
=
=
=
=
−
−
−
−
−
110 1
10
7 7 7 7
6 6 6
107
3 8 3 8 11
2 3 2
−
− − − + −( ) −
− − −
=
⋅ = =
⋅ =
7.
8. ++ −( ) −
− − − − −( ) −
− − +
=
= =
⋅ =
3 5
5 2 5 2 3
8 4 8 4
6
9 9 9 9
3 3 3
9.
10.
÷
==
=
=
−
− − −
− + + − − + −
3 4
2 3 1 5 5 1
2 3 5 1 5 1 6 5
11.
12.
B B C B C C
B C B C
CC D D C D D C
C D C D
1.
2.
3.
4.
5.
6.
1
44
1
77
1
44
1
33
5 1
5
22
22
33
22
33
=
=
=
=
=
−
−
−
−
−
110 1
10
7 7 7 7
6 6 6
107
3 8 3 8 11
2 3 2
−
− − − + −( ) −
− − −
=
⋅ = =
⋅ =
7.
8. ++ −( ) −
− − − − −( ) −
− − +
=
= =
⋅ =
3 5
5 2 5 2 3
8 4 8 4
6
9 9 9 9
3 3 3
9.
10.
÷
==
=
=
−
− − −
− + + − − + −
3 4
2 3 1 5 5 1
2 3 5 1 5 1 6 5
11.
12.
B B C B C C
B C B C
CC D D C D D C
C D C D
− − −
− + + − + − +
=
=
( )
1 5 4 3 2 4 1
1 3 1 5 4 2 4 3 1
5813.44
5 4 20
35
3 5 15
1 2 1
31
8 8
9 9 9
= =
( ) = =
=
×
×
− −
−−
14.
15. A B B
ABA AA B B B
A B
A B B
A
C
− −
− + −( ) + −( )+
−
=
=
1 2 1 3
1 1 2 1 3
2 44
2 or
16.00 3 3
3 40 3 3 3 1 4
0 3 3 3 1 4
B C B
C BC C C B BB
C B
C
−
−− −
+ + − + + −( )
=
=
= 66 66
6B C
B
− or
Lesson Practice 19B1.
2.
3.
4.
5.
1
88
1
55
7 1
7
17
1
4 4
22
33
11
66
8 5
−
−
−
−
−
=
=
= =
=
⋅
XX
== =
⋅ = =
( ) =
− + −
− − − + −( ) −
− − ×
4 4
6 6 6 6
3 3
8 5 3
4 2 4 2 6
32
3 2
6.
7. ==
( ) = =
( ) = =
−
−×− −
− − × −
3
4 4 4
6
45
4 5 20
23
2 3 6
0
8.
9.
10.
A A A
C DD D C C C
C D C D
E F F E F E
−
+ + + − +
− −
=
=
5 6 1 2 3
0 1 2 3 5 6 6 1
0 3 4 5 211. −− + −( )+ −( ) + + −( )
−
−
=
=
6 0 6 5 3 4 2
11 55
11
6
E F
E F or F
E
B12. CC C C C B B C B C BC
Y Y
1 2 3 4 7 6 7 1 2 3 4 1 2 2
10
− − + + + + −( )
−
= = =
⋅13. 55 3 10 5 3 88
8 3 8 3 5
1÷
÷
Y Y Y orY
A A A A
= =
= =
− + − −
−
aLGeBra 1
Lesson Practice 19B - sYsteMatic reVieW 19D
soLutions 225
1.
2.
3.
4.
5.
1
88
1
55
7 1
7
17
1
4 4
=
=
= =
=
⋅ == =
⋅ = =
( ) =
− + −
− − − + −( ) −
− − ×
4 4
6 6 6 6
3 3
8 5 3
4 2 4 2 6
32
3 2
6.
7. ==
( ) = =
( ) = =
−
−×− −
− − × −
3
4 4 4
6
45
4 5 20
23
2 3 6
0
8.
9.
10.
A A A
C DD D C C C
C D C D
E F F E F E
−
+ + + − +
− −
=
=
5 6 1 2 3
0 1 2 3 5 6 6 1
0 3 4 5 211. −− + −( )+ −( ) + + −( )
−
−
=
=
6 0 6 5 3 4 2
11 55
11
6
E F
E F or F
E
B12. CC C C C B B C B C BC
Y Y
1 2 3 4 7 6 7 1 2 3 4 1 2 2
10
− − + + + + −( )
−
= = =
⋅13. 55 3 10 5 3 88
8 3 8 3 5
1÷
÷
Y Y Y orY
A A A AX X X X X
= =
= =
− + − −
−14.
155. X Y X Y
Y Y XX Y X Y Y Y X
X
−
−− − −
− + + −(
=
=
5 2 3 2
3 4 25 2 3 2 3 4 2
5 3 2)) + + + −( )
−
−
−
=
=
Y
X Y or Y
X
A B A B
B A A
2 2 3 4
4 33
4
3 2 5 3
4 3 516. AA B A B B A A
A B
A B
− − −
− + + + −( ) + + −( )== =
3 2 5 3 4 3 5
3 5 3 5 2 3 4
0 1 1BB B=
Systematic Review 19C1.
2.
3.
4.
5.
1
33
2 1
21
77
1
4 4 4
22
44
22
55
5 2 5
=
=
=
=
⋅ =
−
−
−
−
−
YY
++ −( )
− − − + −( ) −
− −
=
⋅ = =
=
2 3
2 6 2 6 8
8 2 3 4 5
4
5 5 5 56.
7. A B A A B
A−− + + − + −
− −
− +
=
=
8 3 4 2 5 1 33
2 3 4 4 2 4
2 4
B A B or BA
D C C D C D
D
8.++ + + −( )
− − + −
=
⋅ = =
=
4 3 4 2 5 6
10 6 10 6 4
5 4
4 4 4 4
C C D
X X X
9.
10. ÷ 55 4 1
32
3 2 6
57
5 7 35
3 3 3
2 2 2
8
−
×
×
= =
( ) = =
( ) = =
−
X X
11.
12.
13. (( ) = −( ) −( ) ==
=−
− −−
2
1 2 3 4
2 3 51
8 8 64
25 514.
15. E F F E
F E EE FF F E F E E
E F
EF EF
2 3 4 2 3 5
1 4 3 5 2 3 2
1 7 7
1
−
− + + + −( ) + +== =
×16. 110 3 10 7 10 8 10
1000 300 7 08 1 307 08
3 2 0 2+ × + × + × =+ + + =
−
−− + + − + −
− −
− +
8 3 4 2 5 1 33
2 3 4 4 2 4
2 4
B A B or BA
D C C D C D
D ++ + + −( )
− − + −
=
⋅ = =
=
4 3 4 2 5 6
10 6 10 6 4
5 4
4 4 4 4
C C D
X X X
9.
10. ÷ 55 4 1
32
3 2 6
57
5 7 35
3 3 3
2 2 2
8
−
×
×
= =
( ) = =
( ) = =
−
X X
11.
12.
13. (( ) = −( ) −( ) ==
=−
− −−
2
1 2 3 4
2 3 51
8 8 64
25 514.
15. E F F E
F E EE FF F E F E E
E F
EF EF
2 3 4 2 3 5
1 4 3 5 2 3 2
1 7 7
1
−
− + + + −( ) + +== =
×16. 110 3 10 7 10 8 10
1000 300 7 08 1 307 08
3 2 0 2+ × + × + × =+ + + =
−
. , .
117.
18.
3 4 2 13 4
3 4 2 13 4
N N N
N N N
( ) + +( ) = − +( )( ) + +( ) = − +( )
33 4 8 13 523 4 13 52 8
20 603 3
N N NN N N
NN
+ + = − −+ + = − −
= −= − − −; 11 1
7
05 10 45
05 10 45 100
;
. . .
. . .
19. N D
N D
N D
+ =+ =
+ =( )( ) =>>+ =( ) −( ) =>
+ =− − = −
==
N D
N D
N D
D
D
7 5
5 10 45
5 5 35
5 10
2
N D NN
X YY X
+ = => + ( ) ==
+ − == − +
7 2 75
5 10 20 010 5 20
20.
YY X= − +12
2
Systematic Review 19D1.
2.
3.
4.
5.
1
44
5 1
51
1 1
55
88
55
11
−
−
−
−
=
=
=
= =
⋅ =
XX
AA A
X XA B XX
E F E F E F E
A B+
− − +
− − + −( )+⋅ = =
=
6.
7.
3 3 3 32 8 2 8 6
0 5 1 2 3 3 0 1 33 5 2 3 2 6
8 5 1 2 6 4 5 6 8 1 2
F E F
C B C C B C B C
+ −( )+
− − + −( ) − + +
=
=8. ++
− −
− − − − −( )
=
= =
4
1 1
3 6 3 6 3
10
1
7 7 7 7
C B orBC
X XY
9.
10.
÷
÷ 55 10 5 5
34
3 4 12
5
10 10 10
1 000
Y Y Y YX X= =
( ) = =
( ) =
−
×11.
12. , 110 10
5 5 5 25
36 6
35
15
2
5 4
( ) =
− = − ×( ) = −
− = −
13.
14.
15.
aLGeBra 1
sYsteMatic reVieW 19D - sYsteMatic reVieW 19e
soLutions226
1.
2.
3.
4.
5.
1
44
5 1
51
1 1
55
88
55
11
−
−
−
−
=
=
=
= =
⋅ =
XX
AA A
X XA B XX
E F E F E F E
A B+
− − +
− − + −( )+⋅ = =
=
6.
7.
3 3 3 32 8 2 8 6
0 5 1 2 3 3 0 1 33 5 2 3 2 6
8 5 1 2 6 4 5 6 8 1 2
F E F
C B C C B C B C
+ −( )+
− − + −( ) − + +
=
=8. ++
− −
− − − − −( )
=
= =
4
1 1
3 6 3 6 3
10
1
7 7 7 7
C B orBC
X XY
9.
10.
÷
÷ 55 10 5 5
34
3 4 12
5
10 10 10
1 000
Y Y Y YX X= =
( ) = =
( ) =
−
×11.
12. , 110 10
5 5 5 25
36 6
35
15
2
5 4
( ) =
− = − ×( ) = −
− = −
13.
14.
15. C D D−−
− −− − −
+ −( )+ + −(
=
=
3
2 1 3 45 4 3 2 1 3 4
5 1 3 4 3
D C C DC D D D C C D
C D))+ + −( )
−
−
= =
× + × + × + ×
2 4
7 17
4 1 12 10 5 10 6 10 9
C D or CD
16. 110
20 000 50 6 09 20 050 69
3 6 2
2− =+ + + =
( ) + +( ) =, . . , .
17. N N 88 4 14
3 6 2 8 4 143 6 12 8 3
N
N N NN N N
+( ) −( ) + +( ) = +( ) −
+ + = +18.
22 143 6 8 32 14 12
6
6 8 10
11
25
−+ − = − −
=
+ =+
N N NN
Q D
Q
; ;
.
19.
.. .
. . .
10 2 15
25 10 2 15 100
11 10
D
Q D
Q D
=
+ =( )( ) =>+ =( ) −( ) =>>
+ =− − = −
==
25 10 215
10 10 110
15 105
7
Q D
Q D
Q
Q
Q D DD
Y X Y X
Y X X
+ = => ( ) + ==
− = => =
− = − => ( ) −
11 7 114
0
3 4
20.
33 42 4
2
0 2 02
XX
X
Y X YY
= −− = −
=
− = => − ( ) ==
Systematic Review 19E 1.
2.
3.
4.
5.
1
77
10 1
101
8 1
8
33
77
2 4
−
−
−
−
−
=
=
=
=
⋅ =
AA
A A
XX
XX
AA A orA
2 4 22
6 4 6 4 2
11 3
1
5 5 5 5
10 10 1
+ −( ) −
−
−
=
= =
⋅
6.
7.
÷
÷ 00 10 105 11 3 5 3
2 3 4 8 2 4
3 4 2
= =
=
+ −( )−
− − −
− + −( )+
8. D C C D C D
C DD C D or D
C
M M M M
X
X X X X
2 8 4 5 66
5
0 1
+ + −( ) −
− − +
=
⋅ = = =9.
10. 22 4 2 4 22
25
32
1
11 11
Y Y Y Y YY
X X X orX
÷ = =
( )
=
− −
11. ×× × =
( ) = ( ) =
( ) = × =
5 3 30
3 23
6
2
11
49 7 7
15 15 15 225
12.
13.
14..
15.
81 9
1 2 4 1
3 41 2 4 1 3 4
1 4 3 2
=
=
=
−
−− −
+ +
X Y X Y
X YX Y X Y X Y
X Y ++ −( )+ −( )
−
−
=
= × + × +
1 4
8 38
3
0 24 093 4 10 9 10
X Y or X
Y
.16. 33 10
2 3 1 2 21
2 3 1
3×( ) + +( ) − +( ) =( ) + +( ) − +
−
17.
18.
N N N
N N N 22 212 3 3 2 21
2 3 21 3 2
4 205
5 6
( ) =+ + − − =
+ − = − +==
N N NN N N
NN
; ;;
. . .
. . .
7
30
25 05 4 30
25 05 4 30 100
19. Q N
Q N
Q N
+ =+ =
+ =( )( )) =>+ =( ) −( ) =>
+ =− − = −
=Q N
Q N
Q N
Q
Q
30 5
25 5 430
5 5 150
20 280
==
+ = => ( ) + ==
= − ++ =
14
30 14 3016
2 9
2 9
Q N NN
Y X
X Y
20.
aLGeBra 1
sYsteMatic reVieW 19e - Lesson Practice 20a
soLutions 227
33 10
2 3 1 2 21
2 3 1( ) + +( ) − +
17.
18.
N N N
N N N 22 212 3 3 2 21
2 3 21 3 2
4 205
5 6
( ) =+ + − − =
+ − = − +==
N N NN N N
NN
; ;;
. . .
. . .
7
30
25 05 4 30
25 05 4 30 100
19. Q N
Q N
Q N
+ =+ =
+ =( )( )) =>+ =( ) −( ) =>
+ =− − = −
=Q N
Q N
Q N
Q
Q
30 5
25 5 430
5 5 150
20 280
==
+ = => ( ) + ==
= − ++ =
14
30 14 3016
2 9
2 9
Q N NN
Y X
X Y
20.
Lesson Practice 20A1. X X2 11 2+ +
2. X X2 6 8+ +
3. X2 8−
4. X X
X X
X X
2
2
2
6 3
3 7 9
4 6
− ++ −+ −
5. X
X X
X X
2
2
2
8
6 7
2 6 15
−
+ −
+ −
6. 2 10 7
2 8 9
4 2 2
2
2
2
X X
X X
X X
+ +− −+ −
7. X X X X+( ) +( ) = + +1 2 3 22
8. X X X X+( ) +( ) = + +4 3 7 122
9. X X X X+( ) +( ) = + +1 5 6 52
10. 11.
3 51
3 2
3 2
3 5 2
5
2
2
XXX
X X
X X
X+× +
+++ +
++× +
+++ +
52
10 10
5 5
5 15 10
2
2
XX
X X
X X
12.. 13
2 15
10 5
2
2 11 5
2
2
XXX
X X
X X
+× +
+++ +
..
14.
XX
X
X X
X X
+× +
+++ +
85
5 40
3
3 29 40
2
2
3
24
XXXX
X X
X X
X+× +
+++ +
+×
313
2 6
2 7 3
3 2
2
2
2
15. 2
XX
X X
X X
XX
++
++ +
+×
13 2
6 4
6 7 2
4 2
2
2
16.+++
++ +
−× +3
12 6
4 2
4 14 6
2 52
2
2
X
X X
X X
XX
17.
3
4 10
2 5
2 10
3 51
2
2
X
X X
X X
XX
−−− −
+× −
aLGeBra 1
Lesson Practice 20a - Lesson Practice 20B
soLutions228
12.. 13
2 15
10 5
2
2 11 5
2
2
XXX
X X
X X
+× +
+++ +
..
14.
XX
X
X X
X X
+× +
+++ +
85
5 40
3
3 29 40
2
2
3
24
XXXX
X X
X X
X+× +
+++ +
+×
313
2 6
2 7 3
3 2
2
2
2
15. 2
XX
X X
X X
XX
++
++ +
+×
13 2
6 4
6 7 2
4 2
2
2
16.+++
++ +
−× +3
12 6
4 2
4 14 6
2 52
2
2
X
X X
X X
XX
17.
3
4 10
2 5
2 10
3 51
2
2
X
X X
X X
XX
−−− −
+× −
18.
−− −−+ −
3 5
9 15
9 5
2
2
X
X X
X X
12
Lesson Practice 20B1. X X2 3 7− −
2. 2 7 32X X− −
3. X X2 5 9+ +
4. X X
X X
X X
2
2
2
3 2
7 12
2 10 14
+ ++ +
+ +
5. X X
X X
X X
2
2
2
6 5
3 2
4 5 3
+ +− −+ +
6. 5 5 10
2 5
7 6 5
2
2
2
X X
X X
X X
− −+ ++ −
11
7. X X X X+( ) +( ) = + +4 5 9 202
8. X X X X+( ) +( ) = + +7 3 10 212
9. X X X X+( ) +( ) = + +4 8 12 322
10.
7 12
14 2
7
7 15 2
2
2
XXX
X X
X X
+× +
+++ +
111. 3 76
18 42
3 7
3 25
2
2
XXX
X X
X X
+× +
+++
++
+× +
+++
42
2 81
2 8
6
6 26
2
2
3
24
12. XXX
X X
X X ++
+× −− −++ −8
83
3 24
5 24
2
2
8
13.
14
XXX
X X
X X
.. 15
2 19
18 9
2
2 17 9
XXX
X X
X X
−× +
−++ −
..
16.
3 52
6 10
3 5
3 11 10
XXX
X X
X X
+× +
+++ +
44 23
12 6
4 2
4 14 6
5
aLGeBra 1
Lesson Practice 20B - sYsteMatic reVieW 20c
soLutions 229
10.
7 12
14 2
7
7 15 2
2
2
XXX
X X
X X
+× +
+++ +
111. 3 76
18 42
3 7
3 25
2
2
XXX
X X
X X
+× +
+++
++
+× +
+++
42
2 81
2 8
6
6 26
2
2
3
24
12. XXX
X X
X X ++
+× −− −++ −8
83
3 24
5 24
2
2
8
13.
14
XXX
X X
X X
.. 15
2 19
18 9
2
2 17 9
2
2
XXX
X X
X X
−× +
−++ −
..
16.
3 52
6 10
3 5
3 11 10
2
2
XXX
X X
X X
+× +
+++ +
44 23
12 6
4 2
4 14 6
5
2
2
XXX
X X
X X
−× −
− +−− +
17. XXXX
X X
X X
+× −− −−− −
23
15 6
15 6
15 6
2
2
3
9
18. 33 72
6 14
12 28
12 34 14
2
2
XXX
X X
X X
+× +
+++ +
4
Systematic Review 20C 1. 3 7 6
2 3
4 9 9
2
2
2
X X
X X
X X
+ ++ ++ +
2. 2 5 1
3 4
3 8 5
2
2
2
X X
X X
X X
+ ++ ++ +
3. 4 8 2
3 1
3 11 1
2
2
2
X X
X X
X X
+ +− + −
+ +
4. X X X X+( ) +( ) = + +4 8 12 322
5. X X X X+( ) +( ) = + +5 2 7 102
6. X X X X+( ) +( ) = + +2 6 8 122
7.
8.
3 62
6 12
3 6
3 12 12
2 5
2
2
XX
X
X X
X X
X
+× +
+++ +
+
× ++
++ +
−× +
X
X
X X
X X
XX
3
6 15
2 5
2 11 15
4 51
2
2
9.
4 5
4 5
4 5
1
1
2
2
44
3
X
X X
X X
XX
X
−−− −
=
=
aLGeBra 1
sYsteMatic reVieW 20c - sYsteMatic reVieW 20D
soLutions230
7.
8.
3 62
6 12
3 6
3 12 12
2 5
2
2
XX
X
X X
X X
X
+× +
+++ +
+
× ++
++ +
−× +
X
X
X X
X X
XX
3
6 15
2 5
2 11 15
4 51
2
2
9.
4 5
4 5
4 5
1
1
2
2
44
3
X
X X
X X
XX
X
−−− −
=
=
−
−
10.
11.XX
A A A A
3
2 0 4 2 4 2
4 7 4 7 3
5 3 5 5 1 512.
13.
× × = × =
= =
− + −( ) −
− −
÷ orA
1
5 5 5
5 5 5
3
25
2 5 10
12 3 4 34
14.
15.
1
( ) = =
( ) = ( ) = ( )×
×
66.
17.
18.
196 14
1
45
5 2 5 2 33
=
× = =
+× +
− − + −C C C C orC
XX
55 20
4
9 20
9 20 6 9
2
2
2 2
X
X X
X X
A X X
+++ +
= + + = ( ) +
19. 66 20
36 54 20 110
4 2
( ) += + + =
+( )( ) =>square units
X
X
20.
++( )( ) =>+
× ++
++
5 2
2 82 10
20 80
4 16
4
2
2
XXX
X X
X
336 80X +
Systematic Review 20D1. X X
X X
X X
2
2
2
3 7
2 4 4
3 11
− −+ −+ −
Systematic Review 20D
2. X X
X X
X X
2
2
2
11 2
3 4 6
4 7 8
+ +
− ++ +
3. X X
X X
X X
2
2
2
10 5
2 14
11 9
− −− − +− − +
4. X X X X+( ) +( ) = + +2 7 9 142
5. 2 3 4 2 11 122X X X X+( ) +( ) = + +
6. X X X X+( ) +( ) = + +1 9 10 92
aLGeBra 1
sYsteMatic reVieW 20D - sYsteMatic reVieW 20e
soLutions 231
7.
8.
2 43
6 12
2 4
2 10 12
3
2
2
XX
X
X X
X X
X
+× +
+++ +
−
114
12 4
3
3 11 4
2 3
2
2
× +−
−+ −
−×
X
X
X X
X X
X9.XX
X
X X
X X
XX
−− +
−− +
= −
4
8 12
2
2 11 12
1
2
2
44
3
10.
11..
12.
13.
1
3 4 4 3 4 3 4 3 4
55
7 3 2 7 3 2 7 1 7
YY
or
−
− + −( )
=
× × = = ×
BB B B B5 1 5 1 4
36
3 6 18
15 3 5
8 8 8
2 2
÷ = =
( ) = =
( ) = ( ) =
−
×
×
14.
15. 22
225 15
35
3 8 7 3 8 7 2
( )=
× × = =− − − + + −( ) −
16.
17. D D D D D or 1
2 44
8 16
2
2 12 16
2
2
2
D
XX
X
X X
X X
18. +× +
+++ +
4
119. A X X= + + =
( ) + ( ) + =( ) + +
2 12 16
2 10 12 10 16
2 100 120 16
2
2
==+ + =
+ ++
200 120 16 336
2 12 162
2
square units
X X
X
20.
33 1
3 15 172
X
X X
++ +
119. A X X= + + =
( ) + ( ) + =( ) + +
2 12 16
2 10 12 10 16
2 100 120 16
2
2
==+ + =
+ ++
200 120 16 336
2 12 162
2
square units
X X
X
20.
33 1
3 15 172
X
X X
++ +
Systematic Review 20E1. X X
X X
X X
2
2
2
3 2
4 3
2 7 1
+ −+ ++ +
2. 3 2 1
2 2 8
5 7
2
2
2
X X
X X
X
+ −− +
+
3. 5 4 7
3 7
4 7 14
2
2
2
X X
X X
X X
+ +− + +
+ +
4. X X X X+( ) +( ) = + +3 3 6 92
aLGeBra 1
sYsteMatic reVieW 20e - Lesson Practice 21a
soLutions232
5. 2 4 2 2 8 82X X X X+( ) +( ) = + +
6. 3 2 3 62X X X X( ) +( ) = +
7.
8.
2 32
4 6
2 3
2 7 6
16
2
2
XXX
X X
X X
XX
−× −− +−− +
−× −
−− +−− +
+× −− −+
6 6
7 6
2 23
6 6
2
2
2
2
X
X X
X X
XXX
X X
2
9.
2 4 6
1
1
7 7 7
2
55
22
2 5 2
X X
XX
YY
− −
=
=
×
−
−
− −
10.
11.
12. ÷ == =
=
( ) =
− + − −( )
−
7 7
5 5
2 5 2 5
7 3 7 37
3
25
13.
14.
A B A B or A
B÷
22 5 10
12 3 4 34
0
5
5 5 5
169 13
×
×
=
( ) = ( ) = ( )− = −
15.
16.
17. C C−− − − + −( )+ + −( )+ −( )
− −
=
=
4 8 7 3 3 0 4 3 8 7 3
1 2 1D D D C C D
C D orCCD
NNN
N
2
3 42 55 9
5 9 5 10 9 50 9 59
18.
19.
20.
++ +
+
+ = ( ) + = + =
22 75
10 35
14
14 59 35
YYY
Y
Y Y
+× +
+++ +
7
49Y
22 5 10
12 3 4 34
0
5
5 5 5
169 13
×
×( ) = ( ) = ( )− = −
15.
16.
17. C C−− − − + −( )+ + −( )+ −( )
− −
=
=
4 8 7 3 3 0 4 3 8 7 3
1 2 1D D D C C D
C D orCCD
NNN
N
2
3 42 55 9
5 9 5 10 9 50 9 59
18.
19.
20.
++ +
+
+ = ( ) + = + =
22 75
10 35
14
14 59 35
2
2
YYY
Y
Y Y
+× +
+++ +
7
49Y
Lesson Practice 21A 1. X
XX
X X
X X
+× +
+++ +
22
2 4
2
4 4
2
2
X + 2( )
X + 2( )
2. XXX
X X
X X
+× +
+++ +
32
2 6
3
5 6
2
2
X +3( )
X + 2( )
3. XXX
X X
X X
+× +
+++ +
101
10
10
11 10
2
2
X +10( )
X +1( )
4. XXX
X X
X X
+× +
+++ +
42
2 8
4
6 8
2
2
X + 2( )
X + 4( )
5. XXX
X X
X X
+× +
+++ +
717
7
8 7
2
2
X +7( )
X +1( )
aLGeBra 1
Lesson Practice 21B - Lesson Practice 21B
soLutions 233
6. XXX
X X
X X
+× +
+++ +
62
2 12
6
8 12
2
2
X + 2( )
X +6( )
7. XXX
X X
X X
+× +
+++ +
11 1
11
11
12 11
2
2 X +11( )
X +1( )
8. XXX
X X
X X
+× +
+++ +
6
16
6
7 6
2
2
X +1( )
X +6( )
9. XXX
X X
X X
+× +
+++ +
7
22 14
7
9 14
2
2
X + 2( )
X +7( )
10. XXX
X X
X X
+× +
+++ +
15
115
15
16 15
2
2
X +15( )
X +1( )
11. XXX
X X
X X
+× +
+++ +
212
2
3 2
2
2
X +1( )
X + 2( )
12. XXX
X X
X X
+× +
+++ +
313
3
4 3
2
2
X +3( )
X +1( )
13. XXX
X X
X X
+× +
+++ +
818
8
9 8
2
2
X +8( )
X +1( )
14. XXX
X X
X X
+× +
+++ +
181
18
18
19 18
2
2
X +18( )
X +1( )
15. XXX
X X
X X
+× +
+++ +
54
4 20
5
9 20
2
2 X + 5
X + 4
( )
( )
16. XXX
X X
X X
+× +
+++ +
7
33 21
7
10 21
2
2 X +7( )
X +3( )
Lesson Practice 21B 1. X
XX
X X
X X
+× +
+++ +
8
22 16
8
10 16
2
2 X +8( )
X + 2( )
2. XXX
X X
X X
+× +
+++ +
8
7
44 28
11 28
2
2 X +7( )
X + 4( )
aLGeBra 1
Lesson Practice 21B - Lesson Practice 21B
soLutions234
3. XXX
X X
X X
+× +
+++ +
11
11
23 22
13 22
2
2 X +11( )
X + 2( )
4. XXX
X X
X X
+× +
+++ +
4
4
33 12
7 12
2
2 X + 4( )
X +3( )
5. XXX
X X
X X
+× +
+++ +
5
5
33 15
8 15
2
2 X + 5( )
X +3( )
6. XXX
X X
X X
+× +
+++ +
6
6
55 30
11 30
2
2
X + 5( )
X +6( )
7. XX
X
X X
X X
+× +
+++ +
4
4
1
4
5 4
2
2 X + 4( )
X +1( )
8. XX
X
X X
X X
+× +
+++ +
5
5
1
5
6 5
2
2 X + 5( )
X +1( )
9. XX
X
X X
X X
+× +
+++ +
4
4
4
4 16
8 16
2
2 X + 4( )
X + 4( )
10. XXX
X X
X X
+× +
+++ +
1
2 20
10
12 20
2
2
0 2
X +10( )
X + 2( )
11. XXX
X X
X X
+× +
+++ +
2
9
2 18
9
11 18
2
2
X + 2( )
X +9( ) 12. X
XX
X X
X X
+× +
+++ +
15
2 30
15
17 30
2
2
2
X + 2( )
X +15( )
13. XXX
X X
X X
+× +
+++ +
2
5
2 10
5
7 10
2
2
X + 2( )
X + 5( )
14. XXX
X X
X X
+× +
+++ +
1
1
2 1
2
2
1
X +1( )
X +1( )
15. XXX
X X
X X
+× +
+++ +
5
5
5
5 25
10 25
2
2 X + 5( )
X + 5( )
aLGeBra 1
Lesson Practice 21B - sYsteMatic reVieW 21c
soLutions 235
16. XXX
X X
X X
+× +
+++ +
25
1
25 25
26 25
2
2
X +1( )
X + 25( )
Systematic Review 21C1. X X X X2 7 12 4 3+ + = +( ) +( )
X + 4( )
X +3( )
2. X X X X2 10 16 8 2+ + = +( ) +( )
X +8( )
X + 2( )
3. X X X2 11 24 8 3+ + = +( ) +( )
X +8( )
X +3( )
4. X X X X2 8 12 6 2+ + = +( ) +( )
X + 2( )
X +6( )
5. XXX
X X
X X
+× +
+++ +
4
2 8
4
6 8
2
2
2
X + 2( )
X + 4( )
6. XXX
X X
X X
+× +
+++ +
3
5
3 15
5
8 15
2
2 X + 5( )
X +3( )
7.
8.
X X X X
XXX
X X
2
2
7 6 6 1
616
6
+ + = +( ) +( )+
× ++
+
X X
X X X X
XXX
2
2
7 6
2 1 1 1
111
+ +
+ + = +( ) +( )+
× ++
9.
10.
X
X X
X X
X X
X
X X
2
2
2
2
2
2 1
2 7 3
5 9
3 2 6
++ +
− −+ +− +
11.
112.
13.
6 2 1
4 3
7 2 4
2
2
2
42
3 1 4 2
X X
X
X X
P P P P
+ +− +− +
( ) = ×− − ×
X
PP
P P
P P orP
R S R
3 1
8 4
8 4 44
2 33
2
1
+
−
− + −
−−
−( )
= ×
= =
( ) =14. −−( ) ( ) −( )
−=
= × =
3 3 3
6 96
9
215 15 15 225
1
S
R S or R
S
15.
16. 66 4
11 2 2 6 4 111 2 4 6 24 1
11 2
=
+ +( ) = +( ) ++ + = + +
+
17. N N NN N N
N NN NNN
D N
− = + −==
+ =( )
6 24 1 47 21
3
3 5 7
10 05 60 10
; ;
. . .
18.
00
9 5
10 5 60
5 5 455 15
3
( ) =>+ =( ) −( ) =>
+ =− − = −
==
D N
D N
D ND
D
D
aLGeBra 1
sYsteMatic reVieW 21c - sYsteMatic reVieW 21D
soLutions236
X
PP
P P
P P orP
R S R
3 1
8 4
8 4 44
2 33
2
+
−
− + −
−−
−( )( ) =14. −−( ) ( ) −( )
−=
= × =
3 3 3
6 96
9
215 15 15 225
1
S
R S or R
S
15.
16. 66 4
11 2 2 6 4 111 2 4 6 24 1
11 2
=
+ +( ) = +( ) ++ + = + +
+
17. N N NN N N
N NN NNN
D N
− = + −==
+ =( )
6 24 1 47 21
3
3 5 7
10 05 60 10
; ;
. . .
18.
00
9 5
10 5 60
5 5 455 15
3
( ) =>+ =( ) −( ) =>
+ =− − = −
==
D N
D N
D ND
D
D ++ = => ( ) + == −=
− = − − + =
N N
NN
X Y or X Y
9 3 9
9 36
7 3 7 3
4
19.
20. YY X Y X< − => < −
( )( ) < ( ) −
<
3 5 34
54
0 0
3 0 5
0
test point :
4 0
,
00 5
0 5
−< − ; false
Y
X
Systematic Review 21D1. X X X X2 11 28 7 4+ + = +( ) +( )
X +7( )
X + 4( )
2. X X X X2 4 4 2 2+ + = +( ) +( )
X + 2( )
X + 2( )
3. X X X X2 6 8 4 2+ + = +( ) +( )
X + 2( )
X + 4( )
4. X X X X2 8 16 4 4+ + = +( ) +( )
X + 4( )
X + 4( )
5.
6.
XXX
X X
X X
XXX
X
+× +
+++ +
+× +
+
515
5
6 5
33
3 9
2
2
22
2
2
3
6 9
12 32 8 4
8
++ +
+ + = +( ) +( )+
×
X
X X
X X X X
X
7.
8.
XX
X X
X X
X X
++
++ +
+ + =
44 32
8
12 32
20 100
2
2
29. XX X
XXX
X X
+( ) +( )+
× ++
+
10 10
1010
10 100
102
10.
X
X X
X X
X
X X
X
2
2
2
2
2
20 100
4
3 3
2 4 1
2
+ +
+ −+ ++ −
11.
12. ++ +− ++ +
( )
=−
× ×
7 6
5 4 10
7 3 16
2
2
53
25 3
X
X
X X
P P
X
13. −− −
−
=2 3030
6 3 20
1
1
P orP
S R S
Anything
aLGeBra 1
sYsteMatic reVieW 21D - sYsteMatic reVieW 21e
soLutions 237
XX
X X
X X
X X
++
++ +
+ + =
12 32
20 100
2
2
29. XX X
XXX
X X
+( ) +( )+
× ++
+
10 10
1010
10 100
102
10.
X
X X
X X
X
X X
X
2
2
2
2
2
20 100
4
3 3
2 4 1
2
+ +
+ −+ ++ −
11.
12. ++ +− ++ +
( )
=−
× ×
7 6
5 4 10
7 3 16
2
2
53
25 3
X
X
X X
P P
X
13. −− −
−
=
( ) =
2 3030
6 3 20
1
1
P orP
S R S
Anything
14.
to the 00 power =
= × =
=
+( )
1
11 11 11 121
144 12
14 2
2
.
15.
16.
17. N ++ ( ) = +( ) −+ + = + −
+ − =
4 12 4 214 28 4 12 48 2
14 4 12 48
N NN N N
N N N −− −==
+ =( )( ) =>
2 286 18
3
3 5 7
10 05 1 80 100
NN
D N
, ,
. . .
18.
DD N
D N
D ND
D
D N
+ =( ) −( ) =>+ =
− − = −==
+
27 5
10 5 180
5 5 1355 45
9
== => ( ) + == −=
= −
27 9 27
27 918
23
N
NN
on
m
19.
20.
the graph
−−( ) = − ( ) +
− = − +
= −
= − −
3 23
3
3 63
1
23
1
b
b
b
Y X
Y
X
#19
#20
Systematic Review 21E1. X X X X2 8 7 7 1+ + = +( ) +( )
X +7( )
X +1( )
2. X X X X2 5 6 3 2+ + = +( ) +( )
X +3( )
X + 2( )
3. X X X X2 9 20 5 4+ + = +( ) +( )
X + 5( )
X + 4( )
4. X X X X2 8 15 5 3+ + = +( ) +( )
X + 5( )
X +3( )
aLGeBra 1
sYsteMatic reVieW 21e - Lesson Practice 22a
soLutions238
5. XXX
X X
X X
+× +
+++ +
19
9 9
10 9
2
2
X +1( )
X +9( )
6. XXX
X X
X X
+× +
+++ +
72
2 14
9 14
2
2
7 X + 2( )
X +7( )
7.
8.
X X X X
XXX
X X
2
2
7 12 3 4
34
4 12
+ + = +( ) +( )+
× ++
+
3
X X
X X X X
XX
2
2
7 12
10 21 3 7
3
+ +
+ + = +( ) +( )+
× +
9.
10.77
7 21
10 21
4 4 1
2
2
2
2
2
3
X
X X
X X
X X
X X
+++ +
− ++ −
11.
11
5 2
2 3 3
7 2
3 10 1
2
2
2
2
30
X X
X X
X X
X X
P
−
+ ++ −+ +
( )
12.
13. PP P P P P P P
S R S R S
4 1 3 0 4 1 0 3 3
2 0 02
5 2 1
− × + −( )
−
= = =
( ) = × ×14. 11
13 1
25
22
5
2 2 5 4 55
4
2
( )= ( )= =
=
−
−
×− −
R
S R
S R S R or R
S
15. 33 13 169
25 5
1 7 2 51 7 14 5
× =
=
+( ) + +( ) = ( )+ + + =
16.
17. N N NN N NN
N N NNN
P N
+ − = − −= −= −
− − −
+
7 5 1 143 15
5
5 4 3
01 05
; ;
. .
18.
==( )( ) =>+ =( ) −( ) =>
+ =− − = −
=
.76 100
20 1
5 76
204 5
P N
P N
P NN 66
14
20 14 2020 146
N
P N PPP
=
+ = => + ( ) == −=
11
13 1
25
22
5
2 2 5 4 55
4
2
= ( )= =
=
−
−
×− −
R
S R
S R S R or R
S
15. 33 13 169
25 5
1 7 2 51 7 14 5
× =
=
+( ) + +( ) = ( )+ + + =
16.
17. N N NN N NN
N N NNN
P N
+ − = − −= −= −
− − −
+
7 5 1 143 15
5
5 4 3
01 05
; ;
. .
18.
==( )( ) =>+ =( ) −( ) =>
+ =− − = −
=
.76 100
20 1
5 76
204 5
P N
P N
P NN 66
14
20 14 2020 146
N
P N PPP
=
+ = => + ( ) == −=
19.
20.
4 3 16
4 3 16
34
4
2 3 2
32
1
Y X
Y X
Y X
Y X
Y X
se
+ == − +
= − +
−
−
≥
≥
ee graph
Y
X
Lesson Practice 22A 1. 2 1
12 1
2
2 3 1
2
2
XXX
X X
X X
+× +
+++ +
X +1( )
2X +1( )
2. 3 14
12 4
3
3 13 4
2
2
XXX
X X
X X
+× +
+++ +
X + 4( )
3X +1( )
aLGeBra 1
Lesson Practice 22a - Lesson Practice 22a
soLutions 239
3. 4 8 4 4 2 1 4 1 12 2X X X X X X+ + = + +( ) = +( ) +( )
XXX
X X
X X
+× +
+++ +
111
2 1
2
2
times 4
X +1( )
X +1( )
4. 2 15
10 5
2
2 11 5
2
2
XXX
X X
X X
+× +
+++ +
X + 5( )
2X +1( )
5. 2 36
12 18
2
2 15 18
2
2
XX
X
X X
X X
+× +
+++ +
3
X +6( )
2X +3( ) 6. 3 1
26 2
3
3 7 2
2
2
XXX
X X
X X
+× +
+++ +
X + 2( )
3X +1( )
7. 2 52
4 10
2
2 9 10
2
2
XXX
X X
X X
+× +
+++ +
5
X + 2( )
2X + 5( )
8. 4 10 4 2 2 5 2 2 2 1 22 2X X X X X X+ + = + +( ) = +( ) +( )
2 12
4 2
2
2 5 2
2
2
XXX
X X
X X
+× +
+++ +
2X +1( )
X + 2( )
tim
es 2
9. 2 33
6 9
2
2 9 9
2
2
XXX
X X
X X
+× +
+++ +
3 X +3( )
2X +3( )
10. 4 12
8 2
4
4 9 2
2
2
XXX
X X
X X
+× +
+++ +
X + 2( )
4X+( )1
11. 3 42
6 8
3
3 10 8
2
2
XXX
X X
X X
+× +
+++ +
4
X +2( )
3X + 4( )
aLGeBra 1
Lesson Practice 22B - Lesson Practice 22B
soLutions240
12. 2 14 20 2 7 10
2 2 5
2 2X X X X
X X
+ + = + +( )= +( ) +( )
XXX
X X
X X
+× +
+++ +
2
25
5 10
7 10
2
2
times 2X + 2( )
X + 5( )
13. 2 13
6 3
2
2 7 3
2
2
XXX
X X
X X
+× +
+++ +
2X +1( )
X +3( )
14. 4 31
4 3
4
4 7 3
2
2
XXX
X X
X X
+× +
+++ +
3
X +1( )
4X +3( )
15. 2 92
4 18
2
2 13 18
2
2
XXX
X X
X X
+× +
+++ +
9
X + 2( )
2X +9( )16. 3 4
39 12
3
3 13 12
2
2
XXX
X X
X X
+× +
+++ +
4
X +3( )
3X + 4( )
Lesson Practice 22B 1.
5
2 51
2 5
2
2 7 5
2
2
XXX
X X
X X
+× +
+++ +
2X + 5( )
X +1( )
2. 5 23
15 6
5
5 17 6
2
2
XXX
X X
X X
+× +
+++ +
2
X +3( ) 5X + 2( )
3.
2 15
10 5
2
2 11 5
2
2
XXX
X X
X X
+× +
+++ +
X + 5( )
2X +1( ) 4. 4 1
312 3
4
4 13 3
2
2
XXX
X X
X X
+× +
+++ +
4X +1( )
X +3( )
5. 2 16 30 2 8 15 2 5 32 2X X X X X X+ + = + +( ) = +( ) +( )
XXX
X X
X X
+× +
+++ +
5
53
3 15
8 15
2
2
times 2
X + 5( )
X +3( )
aLGeBra 1
Lesson Practice 22B - Lesson Practice 22B
soLutions 241
6. 3 9 6 3 3 2 3 1 22 2X X X X X X+ + = + +( ) = +( ) +( )
XXX
X X
X X
+× +
+++ +
1
22 2
3 2
2
2
X +1( )
X + 2( )
times 3
7. 21
2 9
2
2 11 9
2
2
XXX
X X
X X
+× +
+++ +
9
9
X + 1( )
2X +9( )
8. 37
21 14
3
3 23 14
2
2
XXX
X X
X X
+× +
+++ +
1
2
X +7( )
3X + 2( )
9. 25
10 15
2
2 13 15
2
2
XXX
X X
X X
+× +
+++ +
3
3
2X +3( )
X + 5( )
10. 5 10 212( ) + +( ) =X X
7
7
XXX
X X
X X
+× +
+++ +
33 21
10 21
2
2 X +7( )
X +3( )
tim
es 5
11. 6 36 48 6 6 8
6 4 2
2 2X X X X
X X
+ + = ( ) + +( )= +( ) +( )
XXX
X X
X X
+× +
+++ +
4
4
22 8
6 8
2
2
X + 2( )
X + 4( )
times 6
12. 32
6 16
3
3 14 16
2
2
XXX
X X
X X
+× +
+++ +
8
8
X + 2( )
3X +8( )
13. 4 14 6 2 2 7 3
2 2 1 3
2 2X X X X
X X
+ + = ( ) + +( )= +( ) +( )
23
6 3
2
2 7 3
2
2
XXX
X X
X X
+× +
+++ +
1
tim
es 2
2X +1( )
X + 3( )
14. 5
15 2
5
5 7 2
2
2
XXX
X X
X X
+× +
+++ +
2
2
5X + 2( )X +1( )
aLGeBra 1
Lesson Practice 22B - sYsteMatic reVieW 22c
soLutions242
15. 101
10 1
10
10 11 1
2
2
XXX
X X
X X
+× +
+++ +
1
X +1( )
...
......
...
(10X + 1)
16. 45
20 15
4
4 23 15
2
2
XXX
X X
X X
+× +
+++ +
3
3
4X +3( )
X + 5( )
Systematic Review 22C1. 3 4 1X X+( ) +( )
3X + 4( )
X +1( )
2. 2 3 2X X+( ) +( )
X + 2( )
2X + 3( )
3. 23
6 6
2
2 8 6
2
2
XXX
X X
X X
+× +
+++ +
2
2 X + 3( )
2X + 2( )
4. 4
4
22
4 8
2
2 8 8
2
2
XXX
X X
X X
+× +
+++ +
X + 2( )
2X + 4( )
5. 3 4 3X X+( ) +( )
3X + 4( )
X +3( )
6. 4
4
33
9 12
3
3 13 1
2
2
XXX
X X
X X
+× +
+++ + 22
4 24 36 4 6 9
4 3 3
2 27. X X X X
X X
+ + = + +( ) =+( ) +( )
times 4
X +3( )
X +3( )
8. XXX
X X
X X
X X X
+× +
+++ +
+ +( ) = +
3
3
33 9
6 9
4 6 9 4
2
2
2 2 224 36X +
9. 2 1 2 3X X+( ) +( )
2X +1( )
2X +3( )
aLGeBra 1
sYsteMatic reVieW 22D - sYsteMatic reVieW 22D
soLutions 243
10.
11.
23
6 3
4
4 8 3
2
2
2 6
XXX
X X
X X
B B B
+× +
+++ +
× ×
1 2
2
−− + + −( )
+
− −
− −
= =
⋅ =
=
5 2 6 5 3
3 2 1
3 5
B B
A A A
X Y X
Y X
B C B C12.
13. XX Y X Y X
X Y
X Y or XY
A A
− −
− + −( )+ +
−
==
3 2 1 3 5
3 1 5 2 3
1 5 5
314.
22 1
2 43 2 1 2 4
3 2 4 1 2
3 3
B
B AA A BB A
A B
A B o
−− −
+ −( )+ −( ) +
−
=
=
= rr B
A
, ,
3
3
6 4 3 26 10 8 10 2 10 7 106 000 000 80
15. × + × + × + × =+
−
,, , .
, , .
;
000 2 000 07
6 082 000 07
2 3 2
32
1
+ + =
= −
= −
16. Y X
Y X ssee
m
b
bb
Y X or
graph
17. =
( ) = ( ) += +=
= +
32
4 32
0
4 04
32
4 33 2 83 2 8X Y
or X Y− = −
− + =see graph
Y
X
#17 #16
18.
19.
hours amoeba
hours amoeba
1 22 43 84 16
1 2
2 2
3 2
4
1
2
3
22
2
4
620. after 6 hours
2 after X hoursX
Systematic Review 22D1. 3 5 2X X+( ) +( )
X + 2( )
3X + 5( )
2. 4 10 4 2 2 5 2
2 2 1 2
2 2X X X X
X X
+ + = + +( )= +( ) +( )
times 2
2X +1( )
X + 2( )
3. 32
6 6
3
3 9 6
2
2
XXX
X X
X X
+× +
+++ +
3
3
X + 2( )
3X +3( )
aLGeBra 1
sYsteMatic reVieW 22D - sYsteMatic reVieW 22D
soLutions244
4. 23
6 32
XX
X X
+×+
1
2X +1( )
3X( )
5.
6.
3 8 5
3 5 1
3 51
3 5
3
2
2
X X
X X
XXX
X X
+ ++( ) +( )
+× +
++
5
7
3 8 5
4 7 1
4 71
4 7
4
2
2
X X
X X
XXX
X X
+ ++( ) +( )
+× +
++
7.
8.
3
4 11 7
3 2
32
2 6
2
2
X X
X X
XXX
X X
+ ++( ) +( )
+× +
++
9.
10.
X X2 5 6+ +
11.
12.
1
C C C C C orC
− − + + −
−
× × = =
= =
4 3 0 4 3 0 1
5 3 5 3 2
1
8 8 8 8÷
33. B B C
B CB B C B C
B C
B C
5 2 5
4 35 2 5 4 3
5 2 4 5 3
11 2
−
− −−
+ + − +
−
=
=
= or B
C
D C D
D C CD C D D C C
C
11
2
6 4 2
4 0 26 4 2 4 0 2
4
14.−
−− − −
−
=
= ++ −( )+ −( ) + +
−=
=
×
0 2 6 2 4
6 1212
6
86 900 4
8
D
C D or D
C
, .15.
110 6 10 9 10 4 10
3 2 6
23
2
4 3 2 1+ × + × + ×= +
= +
−
16. Y X
Y X
see grapph
17. m
b
b
bb
Y X
=
−
23
3 23
3
3 63
3 21
23
11.
12.
1
× × = =
= =
1
8 8 8 8÷
33. B B C
B CB B C B C
B C
B C
5 2 5
4 35 2 5 4 3
5 2 4 5 3
11 2
−
− −−
+ + − +
−
=
=
= or B
C
D C D
D C CD C D D C C
C
11
2
6 4 2
4 0 26 4 2 4 0 2
4
14.−
−− − −
−
=
= ++ −( )+ −( ) + +
−=
=
×
0 2 6 2 4
6 1212
6
86 900 4
8
D
C D or D
C
, .15.
110 6 10 9 10 4 10
3 2 6
23
2
4 3 2 1+ × + × + ×= +
= +
−
16. Y X
Y X
see grapph
17. m
b
b
bb
Y X
=
−( ) = −( ) +
− = − +
− = − += −
=
23
3 23
3
3 63
3 21
23
−− − =− + = −
1 2 3 32 3 3
or X Yor X Y
see graph
#17
#16
Y
X
18.
19.
weeks dollars
weeks dollars
2 93 274 815 243
1 3
2 3
1
22
3
4
5
20
3 3
4 3
5 3
20 3 3 486 800 00020. weeks (rou= ≈ $ , , , nnded)
May be shown on your
calculator as 3.4868××109
aLGeBra 1
sYsteMatic reVieW 22D - sYsteMatic reVieW 22e
soLutions 245
18.
19.
weeks dollars
weeks dollars
2 93 274 815 243
1 3
2 3
1
22
3
4
5
20
3 3
4 3
5 3
20 3 3 486 800 00020. weeks (rou= ≈ $ , , , nnded)
May be shown on your
calculator as 3.4868××109
Systematic Review 22E 1. 2 3 2 3X X+( ) +( )
2X +3( )
2X +3( )
2. 2 12 16 2 6 8
2 4 2
2 2X X X X
X X
+ + = ( ) + +( ) =( ) +( ) +( )
times 2
X + 4( )
X + 2( )
3. 2 21
2 2
2 2
2 4 2
2
2
XXX
X X
X X
+× +
+++ +
2X + 2( )
X +1( )
4. 2 45
10 20
2 4
2 14 20
2
2
XXX
X X
X X
+× +
+++ +
X + 5( )
2X + 4( )
5. 4 3 2X X+( ) +( )
4X +3( )
X + 2( )
6.
7.
4 32
8 6
4 3
4 11 6
2 1 5
2
2
XXX
X X
X X
X X
+× +
++
+ ++( ) +
(( )+
× ++
++ +
8. 2 15
10 5
2
2 11 5
2
2
XXX
X X
X X
X + 5( )
2X +1( )
9.
10.
X X
XXX
X X
X X
+( ) +( )+
× ++
++ +
3 1
313
4 3
2
2
3 X +1( )
X +3( )
11.
12
B B C B C B C
B C or B
C
2 6 2 5 5 2 6 5 2 5
3 33
3
− − + + −( ) + −( )
−
=
=
..
13.
Y Y Y
D C A
A D CD C A A D C
A A5 5
8 3 2
0 7 28 3 2 0 7 2
⋅ =
=
+
− −
−− − − −
==
=
− + −( ) − + −( ) +
− −
A C D
A C D or D
A C
A
2 0 3 2 8 7
2 5 1515
2 5
14.55 6 7
3 85 6 7 3 8
5 7 3 6 8
D A
C DA D A C D
A C D
A
− −
− −− −
+ −( ) − +
−
=
=
=
( )
22 3 23 2
2
5 0 2 33 10 5 10 2 10 8 10
30
C D or C D
A
15. × + × + × + × =− −
00 000 5 02 008 300 005 028
5 4 10
5 4
, . . , .+ + + =+ == − +
16. Y X
Y X 110
45
2Y X= − +
see graph
aLGeBra 1
sYsteMatic reVieW 22e - Lesson Practice 23a
soLutions246
55 6 7
3 85 6 7 3 8
5 7 3 6 8
D A
C DA D A C D
A C D
A
− −
− −− −
+ −( ) − +
−
=
=
=
( )
22 3 23 2
2
5 0 2 33 10 5 10 2 10 8 10
30
C D or C D
A
15. × + × + × + × =− −
00 000 5 02 008 300 005 028
5 4 10
5 4
, . . , .+ + + =+ == − +
16. Y X
Y X 110
45
2Y X= − +
see graph
Y
X
#16
#17
17. m
b
b
b
Y X or X
=
−( ) = ( ) +
− = +
= −
= −
54
2 54
1
2 54
134
54
134
5 −− =
− + = −
4 13
5 4 13
1 5
Y
or X Y
day grams
(see graph)
18.
22 25
3 125
4 625
1 5
2 5
3 5
4 5
8
1
2
3
4
19.
20.
day grams
days = 55
5
8
Y days Y=
17. m
b
b
b
Y X or X
=
−( ) = ( ) +
− = +
= −
= −
54
2 54
1
2 54
134
54
134
5 −− =
− + = −
4 13
5 4 13
1 5
Y
or X Y
day grams
(see graph)
18.
22 25
3 125
4 625
1 5
2 5
3 5
4 5
8
1
2
3
4
19.
20.
day grams
days = 55
5
8
Y days Y=
Lesson Practice 23A 1. X X
XXX
X X
X
−( ) −( )−
× −− +−−
5 2
52 10
7
2
2
5
5
XX +10
X − 2( )
X − 5( )
2. X X
XXX
X X
X X
−( ) −( )−
× −− +
−− +
6 1
16
7 6
2
2
6
6
X − 6( )
X − 1( )
3. X X
XXX
X X
X X
−( ) −( )−
× −− +−− +
7 2
72
2 14
9
2
2
7
114
X − 2( )
X − 7( )
4. X X
XXX
X X
X X
−( ) −( )−
× −− +−− +
4 3
43
3 12
7
2
2
4
112 X − 4( )
X − 3( )
5. X X
XXX
X X
X X
−( ) −( )−
× −− +
−− +
8 1
818
8
9 8
2
2
X − 8( )
X − 1( )
6. X X
XXX
X X
X X
−( ) −( )−
× −− +
−−
7 3
73
3 21
7
10
2
2
++21 X − 7( )
X − 3( )
aLGeBra 1
Lesson Practice 23a - Lesson Practice 23a
soLutions 247
7. X X
XXX
X X
X
−( ) −( )−
× −− +
−−
9 3
93
3 27
9
12
2
2
XX +27 X − 9( )
X − 3( )
8. X X
XXX
X X
X
−( ) −( )−
× −− +
−−
5 6
56
6 30
5
11
2
2
XX +30 X − 6( )
X − 5( )
9. X X
XXX
X X
X
−( ) −( )−
× −− +−−
9 10
910
10 90
92
2
119 90X + X − 10( )
X − 9( )
10. X X
XXX
X X
X
−( ) −( )−
× −− +
−
11 3
113
3 33
112
2
−− +14 33X
X − 3( )
X − 11( )
11. X X
XXX
X X
X X
+( ) −( )+
× −− −++
7 3
73
3 21
7
4
2
2
−−21
X − 3( )
X + 7( )
12. X X
XXX
X X
X X
+( ) −( )+
× −− −++
7 5
75
5 35
7
2
2
2
−−35
X − 5( )
X + 7( )
13. X X
XXX
X X
X X
+( ) −( )+
× −− −++
6 3
63
3 18
6
3
2
2
−−18
X − 3( )
X + 6( )
14. X X
XXX
X X
X X
−( ) +( )−
× +−
−− −
9 4
94
4 36
9
5
2
2
336
X + 4( )
X − 9( )
15. 2 1 5
2 15
10 5
2
2 9
2
2
X X
XXX
X X
X X
+( ) −( )+
× −− −+−
−−5
X − 5( )
2X + 1( )
16. 2 3 4
2 34
8 12
2 3
2
2
X X
XXX
X X
X
−( ) +( )−
× +−
−
22 5 12− −X
X + 4( )
2X − 3( )
Lesson Practice 23B 1. X X
XXX
X X
X X
−( ) −( )−
× −− +−− +
4 2
22 8
4
6 8
2
2
4
X − 4( )
X − 2( )
aLGeBra 1
Lesson Practice 23a - Lesson Practice 23a
soLutions248
2. X X
XXX
X X
X
−( ) −( )−
× −− +
−−
10 8
88 80
102
2
10
118 80X +
X − 8( )
X −10( )
3. X X
XXX
X X
X
−( ) −( )−
× −− +−−
5 3
53
3 15
5
8
2
2
XX +15
X −3( )
X −5( )
4. X X
XXX
X X
X
−( ) −( )−
× −− +−−
5 4
54
4 20
5
9
2
2
XX +20 X −5( )
X − 4( )
5. X X
XXX
X X
X X
−( ) −( )−
× −− +
−− +
9 1
19
9
10 9
2
2
9
X −9( )
X −1( )
6. X X
XXX
X X
X X
−( ) −( )−
× −− +−− +
1 3
33 3
4 3
2
2
1
X −1( )
X −3( )
7. X X
XXX
X X
X
−( ) −( )−
× −− +
−
11 5
15
5 552
2
1
11
−− +16 55X
X −5( )
X −11( )
8. X X
XXX
X X
X
−( ) −( )−
× −− +
−
12 8
18
8 962
2
2
12
−− +20 96X
X −8( )
X −12( )
9. X X
XXX
X X
X
−( ) −( )−
× −− +
−−
7 6
66 42
1
2
2
7
7
33 42X +
X −6( )
X −7( )
10. X X
XXX
X X
X
−( ) −( )−
× −− +
−−
8 3
33 24
2
2
8
8
111 24X +
X −3( )
X −8( )
11. X X
XXX
X X
X X
+( ) −( )+
× −− −
++ −
3 1
313
2 3
2
2
3
X +3( )
X −1( )
aLGeBra 1
sYsteMatic reVieW 23c - sYsteMatic reVieW 23c
soLutions 249
12. X X
XXX
X X
X
+( ) −( )+
× −− −++
6 3
63
3 182
2
6
33 18X −
X −3( )
X +6( )
13. X X
XXX
X X
X
−( ) +( )−
× +−
−−
5 4
54
4 202
2
5
XX −20 X −5( )
X +4( )
14. X X
XXX
X X
X
+( ) −( )+
× −− −++
5 3
53
3 152
2
5
22
X
X X
XXX
X X
−−( ) +( )
−× +
−+
15
5 1 2
5 12
10 2
5 2
15.
9
5 2
4 1 2
4 12
8 2
4
2
2
X X
X X
XXX
X X
+ −−( ) +( )
−× +
−−
16.
74 22X X+ −
Systematic Review 23C1. X X
XX
X
X X
X X
−( ) +( )−
× +−
−− −
5 2
52
2 10
10
2
2
5
3
Systematic Review 22C 1.
2.
3.
X −5( ) X + 2( ) X − 5
×X + 2
2X −10
X2 −5X
X2 −3X −10
X + 4( ) X −1( ) X +4
×X −1
−X − 4
X2 + 4X
X2 +3X − 4
X − 3
×X − 9
−9X + 27
X
X −5( )
X +2( )
X −1( )
X +4( )
X −3( )
2. X X
XXX
X X
X X
+( ) −( )+
× −− −
++ −
4 1
414
4
2
2
4
3
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
X −5( ) X + 2( ) X − 5
×X + 2
2X −10
X2 −5X
X2 −3X −10
X + 4( ) X −1( ) X +4
×X −1
−X − 4
X2 + 4X
X2 +3X − 4
X − 3
×X − 9
−9X + 27
X2 −3X
X2 −12X + 27
X −3
×X − 3
−3X + 9
X2 −3X
X2 − 6X + 9
X + 2( ) X −1( )
X + 2
×X −1
−X − 2
X2 + 2X
X2 + X − 2
X +5( ) X − 2( )
X +5
×X − 2
−2X −10
X2 +5X
X2 +3X −10
2X +1( ) X +3( )
2X +1
×X +3
6X +3
2X2 + X
2X2 +7X +3
34 ×3−2 ÷33 = 34+ −2( )−3 = 3−1�or�13
7−10
75= 7−107−5 = 7−10+ −5( ) = 7−15�or� 1
715
A5B2A −4
A3B7= A5B2A −4A −3B−7 =
�or� 1
A
X −5( )
X +2( )
X −1( )
X +4( )
X −9( )
X −3( )
X −3( )
X −3( )
3. XX
X
X X
X X
−× −
− +−
− +
39
9 27
12 27
2
2
3
Systematic Review 22C 1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
X −5( ) X + 2( ) X − 5
×X + 2
2X −10
X2 −5X
X2 −3X −10
X + 4( ) X −1( ) X +4
×X −1
−X − 4
X2 + 4X
X2 +3X − 4
X − 3
×X − 9
−9X + 27
X2 −3X
X2 −12X + 27
X −3
×X − 3
−3X + 9
X2 −3X
X2 − 6X + 9
X + 2( ) X −1( )
X + 2
×X −1
−X − 2
X2 + 2X
X2 + X − 2
X +5( ) X − 2( )
X +5
×X − 2
−2X −10
X2 +5X
X2 +3X −10
2X +1( ) X +3( )
2X +1
×X +3
6X +3
2X2 + X
2X2 +7X +3
34 ×3−2 ÷33 = 34+ −2( )−3 = 3−1�or�13
7
X −5( )
X +2( )
X −1( )
X +4( )
X −9( )
X −3( )
X −3( )
X −3( )
4.
5.
XXX
X X
X X
X X
−× −− +−− +
+( ) −( )
33
3 9
6 9
2 1
2
2
3
Systematic Review 22C 1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
X −5( ) X + 2( ) X − 5
×X + 2
2X −10
X2 −5X
X2 −3X −10
X + 4( ) X −1( ) X +4
×X −1
−X − 4
X2 + 4X
X2 +3X − 4
X − 3
×X − 9
−9X + 27
X2 −3X
X2 −12X + 27
X −3
×X − 3
−3X + 9
X2 −3X
X2 − 6X + 9
X + 2( ) X −1( )
X + 2
×X −1
−X − 2
X2 + 2X
X2 + X − 2
X +5( ) X − 2( )
X +5
×X − 2
−2X −10
X2 +5X
X2 +3X −10
2X +1( ) X +3( )
2X +1
×X +3
6X +3
2X2 + X
2X2 +7X +3
34 ×3−2 ÷33 = 34+ −2( )−3 = 3−1�or�13
7
.055
X −5( )
X +2( )
X −1( )
X +4( )
X −9( )
X −3( )
X −3( )
X −3( )
6.
7.
XXX
X X
X X
X X
+× −− −
++ −
+( ) −( )
212
2
5 2
2
2
2
8.
9.
XX
X
X X
X X
X X
+× −
− −++ −+( ) +
52
2 10
3 10
2 1
2
2
5
33( )
10.
11.
2 13
6 3
2
2 7 3
3 3 3
2
2
4 2
XXX
X X
X X
+× +
+++ +
× −
÷ 33 4 2 3 13 3 13
= =+ −( )− − or
12.
13.
7
77 7 7
7 1
7
10
510 5 10 5
1515
5 2
− − − − + −( )
−
= = =
or
A B AA
A BA B A A B
A B A B
− − − −
+ −( )+ −( ) + −( ) −
= =
=
4
3 75 2 4 3 7
5 4 3 2 7 2 −−
− −
− −
−
+ + =
+
52 5
21
1 1
2
2 1
2
1
2 4 3
2 4
orA B
AB B
B A
A
B A
AB
14.
BB B A A B A
AB B A A B
A
− − −
− − + + −( ) −+ =
+ + =
1 1 1 2 2 1
2 1 1 2 1 2
3
2 4 3
2 BB A AB
AB A or A
BA
Y XY X
− −
−
+ + =
+ +
= −= +
2 2
22
4 3
5 4 5 4
43 2
aLGeBra 1
sYsteMatic reVieW 23c - sYsteMatic reVieW 23D
soLutions250
12.
13.
7
77 7 7
7 1
7
10
510 5 10 5
1515
5 2
− − − − + −( )
−
= = =
or
A B AA
A BA B A A B
A B A B
− − − −
+ −( )+ −( ) + −( ) −
= =
=
4
3 75 2 4 3 7
5 4 3 2 7 2 −−
− −
− −
−
+ + =
+
52 5
21
1 1
2
2 1
2
1
2 4 3
2 4
orA B
AB B
B A
A
B A
AB
14.
BB B A A B A
AB B A A B
A
− − −
− − + + −( ) −+ =
+ + =
1 1 1 2 2 1
2 1 1 2 1 2
3
2 4 3
2 BB A AB
AB A or A
BA
Y XY X
− −
−
+ + =
+ +
= −= +
2 2
22
4 3
5 4 5 4
43 2
15.77 3 4 2 7
12 2 714 7
12
4 4
=> −( ) = +− = +− =
= −
= − => = − −
X XX XX
X
Y X Y 112
2
12
2
7 2 2 6 4
=
−
+( ) + ( ) − +( ) = −
Y
N N N
,
16. 117 14 2 6 24 1
7 2 6 1 14 243 9
3
3 5
N N NN N N
NN
+ + − − = −+ − = − − +
==
, ,,
. . .
7
10 05 95 100
12 5
10
17.
D N
D N
D+ =( )( ) =>+ =( ) −( ) =>
+55 955 5 60
5 35
7
12 7 125
ND N
D
D
D N NN
=− − = −
==
+ = => ( ) + ==
188.
19.
23
56
12
23
65
12
25
100 2 02 1 4 2
2
÷ × = × × =
− + =( )(. . .X X .. )09
20 2 140 20918 209 14018 69
6918
236
X XXX
X
− + == −=
= = = 33 56
5 12
5 5 055
055 400 22
20. % . % .
.
= =
× =
188.
19.
23
56
12
23
65
12
25
100 2 02 1 4 2
× = × × =
− + =( )(. . .X X .. )09
20 2 140 20918 209 14018 69
6918
236
X XXX
X
− + == −=
= = = 33 56
5 12
5 5 055
055 400 22
20. % . % .
.
= =
× =
Systematic Review 23D 1.
2.
X X
XX
X
X X
X X
X X
X
−( ) +( )−
× +
−−
− −−( ) +( )
−
2 1
21
2
2
2
1 3
2
2
113
3 3
2 3
2
2
× +
−−
+ −
X
X
X X
X X
Systematic Review 22D 1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
X − 2( ) X + 1( ) X − 2
× X + 1
X − 2
X2 − 2X
X2 − X − 2
X − 1( ) X + 3( ) X − 1
× X + 3
3X − 3
X2 − X
X2 + 6X − 3
X − 3
× X + 9
9X − 27
X2 − 3X
X2 + 6X − 27
X − 5
× X + 6
6X − 30
X2 − 5X
X2 + X − 30
X − 4( ) X + 1( )
X − 4
× X + 1
X − 3
X2 − 4X
X2 − 3X − 4
X − 3( ) X + 1( )X − 3
× X + 1
X − 3
X2 − 3X
X2 − 2X − 3
X − 3( ) X + 2( )X − 3
× X + 2
2X
X +1( )
X −3( )
X +9( )
X −2( )
X +3( )
X −1( )
X −5( )
X +6( )
1.
2.
X X
XX
X
X X
X X
X X
X
−( ) +( )−
× +
−−
− −−( ) +( )
−
2 1
21
2
2
2
1 3
2
2
113
3 3
2 3
2
2
× +
−−
+ −
X
X
X X
X X
Systematic Review 22D 1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
X − 2( ) X + 1( ) X − 2
× X + 1
X − 2
X2 − 2X
X2 − X − 2
X − 1( ) X + 3( ) X − 1
× X + 3
3X − 3
X2 − X
X2 + 6X − 3
X − 3
× X + 9
9X − 27
X2 − 3X
X2 + 6X − 27
X − 5
× X + 6
6X − 30
X2 − 5X
X2 + X − 30
X − 4( ) X + 1( )
X − 4
× X + 1
X − 3
X2 − 4X
X2 − 3X − 4
X − 3( ) X + 1( )X − 3
× X + 1
X − 3
X2 − 3X
X2 − 2X − 3
X − 3( ) X + 2( )X − 3
× X + 2
2X
X +1( )
X −3( )
X +9( )
X −2( )
X +3( )
X −1( )
X −5( )
X +6( )
3.
4.
XX
X
X X
X X
XX
X
X X
X
−× +
−−
+ −−
× +
−−
39
9 27
3
6 27
56
6 30
5
2
2
2
22 30+ −X
Systematic Review 22D 1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
X − 2( ) X + 1( ) X − 2
× X + 1
X − 2
X2 − 2X
X2 − X − 2
X − 1( ) X + 3( ) X − 1
× X + 3
3X − 3
X2 − X
X2 + 6X − 3
X − 3
× X + 9
9X − 27
X2 − 3X
X2 + 6X − 27
X − 5
× X + 6
6X − 30
X2 − 5X
X2 + X − 30
X − 4( ) X + 1( )
X − 4
× X + 1
X − 3
X2 − 4X
X2 − 3X − 4
X − 3( ) X + 1( )X − 3
× X + 1
X − 3
X2 − 3X
X2 − 2X − 3
X − 3( ) X + 2( )X − 3
× X + 2
2X
X +1( )
X −3( )
X +9( )
X −2( )
X +3( )
X −1( )
X −5( )
X +6( )
3.
4.
XX
X
X X
X X
XX
X
X X
X
−× +
−−
+ −−
× +
−−
39
9 27
3
6 27
56
6 30
5
2
2
2
22 30+ −X
Systematic Review 22D 1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
X − 2( ) X + 1( ) X − 2
× X + 1
X − 2
X2 − 2X
X2 − X − 2
X − 1( ) X + 3( ) X − 1
× X + 3
3X − 3
X2 − X
X2 + 6X − 3
X − 3
× X + 9
9X − 27
X2 − 3X
X2 + 6X − 27
X − 5
× X + 6
6X − 30
X2 − 5X
X2 + X − 30
X − 4( ) X + 1( )
X − 4
× X + 1
X − 3
X2 − 4X
X2 − 3X − 4
X − 3( ) X + 1( )X − 3
× X + 1
X − 3
X2 − 3X
X2 − 2X − 3
X − 3( ) X + 2( )X − 3
× X + 2
2X
X +1( )
X −3( )
X +9( )
X −2( )
X +3( )
X −1( )
X −5( )
X +6( )5.
6.
7.
X X
XX
X
X X
X X
X X
−( ) +( )−
× +
−−
− −−( ) +(
4 1
41
4
4
3 4
3 1
2
2
))−
× +
−−
− −−( ) +( )
−× +
8.
9.
10.
XX
X
X X
X X
X X
XX
31
3
3
2 3
3 2
3
2
2
22
2 6
3
6
10 10 10
5
2
2
27
2 7 14
24
X
X X
X X
−−
− −
aLGeBra 1
sYsteMatic reVieW 23D - sYsteMatic reVieW 23e
soLutions 251
5.
6.
7.
X X
XX
X
X X
X X
X X
−× +
−−
− −−( ) +(
4 1
41
4
4
3 4
3 1
2
2
))−
× +
−−
− −−( ) +( )
−× +
8.
9.
10.
XX
X
X X
X X
X X
XX
31
3
3
2 3
3 2
3
2
2
22
2 6
3
6
10 10 10
5
2
2
27
2 7 14
24
X
X X
X X
−−
− −
( ) = =
( )
×11.
12. = =
=
× ×
− −
−− − −
32 4 3 24
4 3 2
4 54 3 2 4 5
5 5
13. D D D
D DD D D D D
== =
+ +
− + + −( )+ −( )+ −
−
−
D D orD
BB B
B
B
4 3 2 4 5 22
21
4
1
3 514.44
1
1 2 1 4 4 1
1 2 1 4 4 1
3
3 5
3 5
3
B
BB B B B B
B B B
B B
−
−
+ − + +
=
+ + =+ + =
+ 33 5 3 55 4 5+ = +B B B
15. Y X
Y X X X
X X
= − +
= − => − +( ) = −− + = −
+
4 5
2 4 3 2 4 5 4 3
8 10 4 310 3 == +
=
= =
= − + => = −
4 813 121312
1 112
4 5 4 1312
X XX
X
Y X Y ++
= − +
= − + =
+(
5
5212
5
133
153
23
1312
23
4 1
Y
Y
N
,
16. )) + +( ) − ( ) + =+ + + − + =
+ − = −
3 2 8 11 04 4 3 6 8 11 0
4 3 8 4
N NN N N
N N N −− −− = −
=
+ =( )
6 1121
21
21 22 23
10 05 3 30 10
NN
D N
; ;
. . .17. 00
10 5 330
45 5 5 5 225
5 105
( )=> + =
+ =( ) −( ) => − − = −=
D N
D N D N
D
DD
D N N
N
=
+ =( ) => ( ) + ==
× = × ×
21
45 21 45
24
12
12
34
12
21
3
== +=
= =
= − + => = −
4 813 121312
1 112
4 5 4 1312
X XX
X
Y X Y ++
= − +
= − + =
+(
5
5212
5
133
153
23
1312
23
4 1
Y
Y
N
,
16. )) + +( ) − ( ) + =+ + + − + =
+ − = −
3 2 8 11 04 4 3 6 8 11 0
4 3 8 4
N NN N N
N N N −− −− = −
=
+ =( )
6 1121
21
21 22 23
10 05 3 30 10
NN
D N
; ;
. . .17. 00
10 5 330
45 5 5 5 225
5 105
( )=> + =
+ =( ) −( ) => − − = −=
D N
D N D N
D
DD
D N N
N
=
+ =( ) => ( ) + ==
× = × ×
21
45 21 45
24
12
12
34
12
21
318. ÷44
34
100 1 03 2 73 45
103 20 73 4
=
( ) + − =( )+ − =
19. . . . .X X X
X X X 5550 45
4550
910
9
5 25
5 4 054
054 2
X
X or
=
= =
= =
×
.
% . % .
.
20.
550 13 5= .
Systematic Review 23ESystematicReview 22E1. X X
XX
X
X
−( ) +( )−
× +
−−
3 1
31
3
32 XX
X X
X X
XX
X
X X
X X
X
2
2
2
2 3
4 1
41
4
4
3 4
− −+( ) −( )
+× −
− −+
+ −
2.
3. −−× +
−−
− −−
× +
−−
+
42
2 8
4
2 8
35
5 15
3
2
2
2
2
2
X
X
X X
X X
XX
X
X X
X X
4.
−−−( ) −( )
−× −
− +−
− +
15
5 2
52
2 10
5
7 10
3
5.
6.
7.
X X
XX
X
X X
X X
XX X
XX
X
X X
X X
X
Systematic Review 22E 1.
2.
3.
4.
X −3( ) X +1( ) X −
×X + 1
X −3
X2 −3X
X2 − 2X −3
X + 4( ) X −1( )
X +
×X −
− X − 4
X2 + 4X
X2 +3X − 4
X − 4
×X + 2
2X − 8
X2 − 4X
X2 − 2X − 8
X − 3
×X + 5
5X −15
X2 −3X
X2 + 2X −15
X
X +1( )
X −3( )
X −1( )
X +4( )
X +2( )
X −4( )
X +5( )
X −3( )
SystematicReview 22E1. X X
XX
X
X
−( ) +( )−
× +
−−
3 1
31
3
32 XX
X X
X X
XX
X
X X
X X
X
2
2
2
2 3
4 1
41
4
4
3 4
− −+( ) −( )
+× −
− −+
+ −
2.
3. −−× +
−−
− −−
× +
−−
+
42
2 8
4
2 8
35
5 15
3
2
2
2
2
2
X
X
X X
X X
XX
X
X X
X X
4.
−−−( ) −( )
−× −
− +−
− +
15
5 2
52
2 10
5
7 10
3
5.
6.
7.
X X
XX
X
X X
X X
XX X
XX
X
X X
X X
X
Systematic Review 22E 1.
2.
3.
4.
X −3( ) X +1( ) X −
×X + 1
X −3
X2 −3X
X2 − 2X −
X + 4( ) X −1( )
X +
×X −
− X − 4
X2 + 4X
X2 +3X − 4
X − 4
×X + 2
2X − 8
X2 − 4X
X2 − 2X − 8
X − 3
×X + 5
5X −15
X2 −3X
X2 + 2X −15
X
X +1( )
X −3( )
X −1( )
X +4( )
X +2( )
X −4( )
X +5( )
X −3( )
aLGeBra 1
sYsteMatic reVieW 23e - Lesson Practice 24a
soLutions252
XX
X X
X X
XX
X
X X
X X
X
2
2
2
2 3
4 1
41
4
4
3 4
− −+( ) −( )
+× −
− −+
+ −
2.
3. −−× +
−−
− −−
× +
−−
+
42
2 8
4
2 8
35
5 15
3
2
2
2
2
2
X
X
X X
X X
XX
X
X X
X X
4.
−−−( ) −( )
−× −
− +−
− +
15
5 2
52
2 10
5
7 10
3
2
2
5.
6.
7.
X X
XX
X
X X
X X
XX X
XX
X
X X
X X
X
−( ) −( )−
× −
− +−
− +
+
7 1
3 71
3 7
3 7
3 10 7
3
2
2
2
8.
9. 115 18 3 5 6 3 6 1
61
6
2
2
X X X X X
XX
X
X
− = + −( ) = +( ) −( )+
× −
− −
10.
++
+ −
+ −( )( ) = + −
6
5 6
5 6 3 3 15 18
2
2 2
X
X X
X X X X
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
3
X + 4( ) X −1( )
X + 4
×X − 1
− X − 4
X2 + 4X
X2 +3X − 4
X − 4
×X + 2
2X − 8
X2 − 4X
X2 − 2X − 8
X − 3
×X + 5
5X −15
X2 −3X
X2 + 2X −15
X −5( ) X − 2( )
X −5
×X − 2
− 2X +10
X2 −5X
X2 −7X +10
3X −7( ) X −1( )
3X −7
×X − 1
−3X +7
3X2 − 7X
3X2 −10X +7
3X2 +15X −18 = 3 X2 +5X − 6( ) =3 X + 6( ) X −1( )
X + 6
×X −1
2X − 6
X2 + 6X
X2 +5X − 6
X2 +5X − 6( ) 3( ) = 3X2 +15X −18
54 ×5−6 ÷52 = 54+ −6( )−2 = 5−4�or� 1
54
16−1
= 61 = 6
4Q−1Y−2 + 5QY−3
Q−1Y−2= 4Q−1Y−2 +5QY−3Q1Y2 =
4Q−1Y−2 +5Q1+1Y−3+2 = 4Q−1Y−2 +5Q2Y−1�or�
4QY2
+ 5Q2
Y
5M4N2M−1 + 2NM4
=
6.46
X
X −1( )
X +4( )
X +2( )
X −4( )
X +5( )
X −3( )
XX
X X
X X
XX
X
X X
X X
X
2
2
2
2 3
4 1
41
4
4
3 4
− −+( ) −( )
+× −
− −+
+ −
2.
3. −−× +
−−
− −−
× +
−−
+
42
2 8
4
2 8
35
5 15
3
2
2
2
2
2
X
X
X X
X X
XX
X
X X
X X
4.
−−−( ) −( )
−× −
− +−
− +
15
5 2
52
2 10
5
7 10
3
2
2
5.
6.
7.
X X
XX
X
X X
X X
XX X
XX
X
X X
X X
X
−( ) −( )−
× −
− +−
− +
+
7 1
3 71
3 7
3 7
3 10 7
3
2
2
2
8.
9. 115 18 3 5 6 3 6 1
61
6
2
2
X X X X X
XX
X
X
− = + −( ) = +( ) −( )+
× −
− −
10.
++
+ −
+ −( )( ) = + −
6
5 6
5 6 3 3 15 18
2
2 2
X
X X
X X X X
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
3
X + 4( ) X −1( )
X + 4
×X − 1
− X − 4
X2 + 4X
X2 +3X − 4
X − 4
×X + 2
2X − 8
X2 − 4X
X2 − 2X − 8
X − 3
×X + 5
5X −15
X2 −3X
X2 + 2X −15
X −5( ) X − 2( )
X −5
×X − 2
− 2X +10
X2 −5X
X2 −7X +10
3X −7( ) X −1( )
3X −7
×X − 1
−3X +7
3X2 − 7X
3X2 −10X +7
3X2 +15X −18 = 3 X2 +5X − 6( ) =3 X + 6( ) X −1( )
X + 6
×X −1
2X − 6
X2 + 6X
X2 +5X − 6
X2 +5X − 6( ) 3( ) = 3X2 +15X −18
54 ×5−6 ÷52 = 54+ −6( )−2 = 5−4�or� 1
54
16−1
= 61 = 6
4Q−1Y−2 + 5QY−3
Q−1Y−2= 4Q−1Y−2 +5QY−3Q1Y2 =
4Q−1Y−2 +5Q1+1Y−3+2 = 4Q−1Y−2 +5Q2Y−1�or�
4QY2
+ 5Q2
Y
5M4N2M−1 + 2NM4
N−3M=
6.46
X
X −1( )
X +4( )
X +2( )
X −4( )
X +5( )
X −3( )
XX
X X
X X
XX
X
X X
X X
X
2
2
2
2 3
4 1
41
4
4
3 4
− −+( ) −( )
+× −
− −+
+ −
2.
3. −−× +
−−
− −−
× +
−−
+
42
2 8
4
2 8
35
5 15
3
2
2
2
2
2
X
X
X X
X X
XX
X
X X
X X
4.
−−−( ) −( )
−× −
− +−
− +
15
5 2
52
2 10
5
7 10
3
2
2
5.
6.
7.
X X
XX
X
X X
X X
XX X
XX
X
X X
X X
X
−( ) −( )−
× −
− +−
− +
+
7 1
3 71
3 7
3 7
3 10 7
3
2
2
2
8.
9. 115 18 3 5 6 3 6 1
61
6
2
2
X X X X X
XX
X
X
− = + −( ) = +( ) −( )+
× −
− −
10.
++
+ −
+ −( )( ) = + −
6
5 6
5 6 3 3 15 18
2
2 2
X
X X
X X X X
XX
X X
X X
XX
X
X X
X X
X
2
2
2
2 3
4 1
41
4
4
3 4
− −+( ) −( )
+× −
− −+
+ −
2.
3. −−× +
−−
− −−
× +
−−
+
42
2 8
4
2 8
35
5 15
3
2
2
2
2
2
X
X
X X
X X
XX
X
X X
X X
4.
−−−( ) −( )
−× −
− +−
− +
15
5 2
52
2 10
5
7 10
3
2
2
5.
6.
7.
X X
XX
X
X X
X X
XX X
XX
X
X X
X X
X
−( ) −( )−
× −
− +−
− +
+
7 1
3 71
3 7
3 7
3 10 7
3
2
2
2
8.
9. 115 18 3 5 6 3 6 1
61
6
2
2
X X X X X
XX
X
X
− = + −( ) = +( ) −( )+
× −
− −
10.
++
+ −
+ −( )( ) = + −
6
5 6
5 6 3 3 15 18
2
2 2
X
X X
X X X X
11.
12.
13
5 5 5 5 5 1
51
66 6
4 6 2 4 6 2 44
11
× = =
= =
− + −( )− −
−
÷ or
.. 4 5
4 5
4
1 23
1 2
1 2 3 1 2
1 2
Q Y QY
Q Y
Q Y QY Q Y
Q Y
− − −
− −
− − −
− −
+ =
+ =
++ =
+ +
+ − +
− − −
5
4 5 4 5
5
1 1 3 2
1 2 2 12
2
4
Q Y
Q Y Q Y orQY
QY
M N14. 22 14
3
4 1 2 1 4 3 1
3 2 3
2
5 2
5 2
M NM
N M
M N NM N M
M N M N
−−
+ −( ) −
+ =
+ =
+ 44
2
3 18
4 16
4
2 4 24 2
15. X Y
X Y
X
X
X Y YY
− = −+ =
==
− = − =>
11.
12.
13.. 4 5
4 5
4
1 23
1 2
1 2 3 1 2
1 2
Q Y QY
Q Y
Q Y QY Q Y
Q Y
− − −
− −
− − −
− −
+ =
+ =
++ =
+ +
+ − +
− − −
5
4 5 4 5
5
1 1 3 2
1 2 2 12
2
4
Q Y
Q Y Q Y orQY
QY
M N14. 22 14
3
4 1 2 1 4 3 1
3 2 3
2
5 2
5 2
M NM
N M
M N NM N M
M N M N
−−
+ −( ) −
+ =
+ =
+ 44
2
3 18
4 16
4
2 4 24 2
15. X Y
X Y
X
X
X Y YY
− = −+ =
==
− = − => ( ) − = −+ =
66
11 2 2 6 4 111 2 4 6 24 1
11
=
( ) + +( ) = +( ) ++ + = + +
Y
N N NN N N
N
16.
++ − = + −==
+ =(
2 6 24 1 47 21
3
3 5 7
25 10 2 00
N NN
N
Q D
; ;
. . .
17.
))( ) =>+ =( ) −( ) =>
+ =− − = −
100
14 25
25 10 200
25 25 35Q D
Q D
Q D 00
15 150
10
14 10 14
4
37
1415
1
− = −=
+ = => + ( ) ==
×
D
D
Q D Q
Q
18. ÷22
37
1415
21
45
36 8 20 1236 12 20 8
24
2
5= × × =
− = +− = +
19. F FF F
==
= =
=× =
282428
67
6 8 068
068 95 6 46
F
F
20. . % .
. .
Lesson Practice 24A1. X X X
XXX
X X
X
2
2
2
4 4 2
22
2 4
4
+ + = +
+× +
+++
check:
2
XX
X X X
XXX
X X
+
+ + = +
+× +
++
4
6 9 3
33
3 9
2
2
2.
check:
3
XX X
X X X
XXX
2
2
6 9
10 25 5
55
5 2
+ +
+ + = +
+× +
+
3.
check:
55
10 25
aLGeBra 1
Lesson Practice 24a - Lesson Practice 24a
soLutions 253
1. X X X
XXX
X X
X
2
2
2
4 4 2
22
2 4
4
+ + = +
+× +
+++
check:
2
XX
X X X
XXX
X X
+
+ + = +
+× +
++
4
6 9 3
33
3 9
2
2
2.
check:
3
XX X
X X X
XXX
2
2
6 9
10 25 5
55
5 2
+ +
+ + = +
+× +
+
3.
check:
55
10 25
2
2
X X
X X
++ +
5
4. X
X X X
X X
X
X
c X
+
+ + +
− +( )+
− +( )
+×
2
3 5 6
3
2 6
2 6
0
2
2
2
heck:
2
XX
X X
X X
++
++ +
33 6
5 6
2
2
5. X R
X X X
X X
X
X
+
+ + +
− +( )+
− +( )
6 6
5 11 36
5
6 36
6 30
6
2
2
checck:
X
X
X
X X
X X
X X
+× +
+
+
+ ++
+ +
6
5
5 30
6
11 30
6
11 36
2
2
2
6. X
X X X
X X
X
X
X
+
+ + +
− +( )+
− +( )
+
4
3 7 12
3
4 12
4 120
2
2
check:
443
3 12
4
7 12
2
8 10 16
8
2
2
2
2
× +
+
+
+ ++
+ + +
− +
X
X
X X
X X
X
X X X
X
7.
XX
X
X
X
X
X
X X
X X
( )+
− +( )
+× +
++
+
2 16
2 16
0
2
8
8 16
2
10
2
2
check:
+++
+ + +
− +( )+
− +( )
16
7
3 10 21
3
7 21
7 21
0
2
2
8. X
X X X
X X
X
X
checck:
XX
X
X X
X X
X
X X X
+× +
+
+
+ ++
+ + +
73
3 21
7
10 21
2 1
3 2 7
2
2
2
9.
33
2 6
3
3
0
2 13
6 3
2
2
2
2
2
− +( )+
− +( )
+× +
+
+
X X
X
X
XX
X
X X
X
check:
++ +7 3X
aLGeBra 1
Lesson Practice 24a - Lesson Practice 24B
soLutions254
X
X X X
X X
X
X
checck:
XX
X
X X
X X
X
X X X
+× +
+
+
+ ++
+ + +
73
3 21
7
10 21
2 1
3 2 7
2
2
2
9.
33
2 6
3
3
0
2 13
6 3
2
2
2
2
2
− +( )+
− +( )
+× +
+
+
X X
X
X
XX
X
X X
X
check:
++ +7 3X
10. X X
X X X X
X X
X X
X
2
3 2
3 2
2
2
5 7
4 9 27 28
4
5 27
5
+ +
+ + + +
− +( )+
− ++( )+
− +( )
+ +× +
+ +
20
7 28
7 28
0
5 7
4
4 20 22
X
X
X
X
X
X X
check:
X2
88
5 7
9 27 28
3 9
1 4 12
3 2
3 2
2
3 2
X X X
X X X
X X
X X X
+ +
+ + +
+ +
+ + +
11.
XX
X X
X X
X X
X
X
+
− +( )+
− +( )+
− +( )
9
3 12
3 3
9 9
9 9
0
3 2
2
2
check:
X22 + +× +
+ +
+ +
+ + +
3 9
1
3 9
3 9
4 12 9
2
3 2
3 2
X
X
X X
X X X
X X X
+ +× +
+ +
20
7 28
7 28
0
5 7
4
4 20 22
X
X
X
X
X
X X
check:
X2
88
5 7
9 27 28
3 9
1 4 12
3 2
3 2
2
3 2
X X X
X X X
X X
X X X
+ +
+ + +
+ +
+ + +
11.
XX
X X
X X
X X
X
X
+
− +( )+
− +( )+
− +( )
9
3 12
3 3
9 9
9 9
0
3 2
2
2
check:
X22 + +× +
+ +
+ +
+ + +
3 9
1
3 9
3 9
4 12 9
2
3 2
3 2
X
X
X X
X X X
X X X
Lesson Practice 24B1. X X X
XX
X
X X
X X
2
2
2
12 36 6
66
6 36
6
12 36
+ + = +
+× +
+
+
+ +
check:
2. X X X
XX
X
X X
X X
2
2
2
14 49 7
77
7 49
7
14 49
+ + = +
+× +
+
+
+ +
check:
3. 4 4 1 2 1
2 1
2 1
2 1
4 2
4 4
2
2
2
X X X
X
X
X
X X
X X
+ + = +
+× +
+
+
+ +
check:
11
aLGeBra 1
Lesson Practice 24B - Lesson Practice 24B
soLutions 255
4. X
X X X
X X
X
X
X
+
+ + +
− +( )+
− +( )
7
3 10 21
3
7 21
7 210
2
2
check:
++× +
++
+ +
73
3 21
7
10 21
2
2
X
X
X X
X X
5. X
X X X
X X
X
X
X
+
+ + +
− +( )+
− +( )
+
5
2 7 10
2
5 10
5 10
0
2
2
check:
55
2
2 10
5
7 10
2
2
× ++
+
+ +
X
X
X X
X X
6. X
X X X
X X
X
X
X
X
+
+ + +
− +( )+
− +( )
+× +
6
1 7 6
6 6
6 6
0
6
2
2
check:
11
6
6
7 6
2
2
X
X X
X X
+
+
+ +
7. X
X X X
X X
X
X
+
+ + +
− +( )+
− +( )
5
3 2 8 15
2 3
5 15
5 15
0
checkk:
X
X
X
X X
X X
+× +
+
+
+ +
5
3
3 15
2 5
2 8 15
8. X
X X X
X X
XX
X
+
+ + +
− +( )+
− +( )
+
5
4 9 20
4
5 205 20
0
2
2
check:
554
4 20
5
9 20
2
2
× +
++
+ +
X
X
X X
X X
9. X
X X X
X X
X
X
X
X
+
− + −
− −( )−
− −( )
+× −
3
2 6
2
3 6
3 6
0
3
2
2
check:
22
2 6
3
6
3 5
2 5 11 10
2
2
2
3 2
− −
+
+ −
− +
− − + −
−
X
X X
X X
X X
X X X X
X
10.
33 2
2
2
2
3 11
3 6
5 10
5 10
0
−( )− +
− − +( )−
− −( )
X
X X
X X
X
X
X
check:22
2
3 2
3 2
3 52
2 6 10
3 5
5 11 10
− +× −
− + −
− +
− + −
XX
X X
X X X
X X X
X
aLGeBra 1
Lesson Practice 24B - sYsteMatic reVieW 24c
soLutions256
X
X X X
X X
X
X
X
X
+× −
3
2 6
2
3 6
3 6
0
3
check:
22
2 6
3
6
3 5
2 5 11 10
2
2
2
3 2
− −
+
+ −
− +
− − + −
−
X
X X
X X
X X
X X X X
X
10.
33 2
2
2
2
3 11
3 6
5 10
5 10
0
−( )− +
− − +( )−
− −( )
X
X X
X X
X
X
X
check:22
2
3 2
3 2
3 52
2 6 10
3 5
5 11 10
− +× −
− + −
− +
− + −
XX
X X
X X X
X X X
X11. 22
3 2
3 2
2
2
4 7 5
3 19 26
3
4 19
4
+ −
− + − +
− −( )−
−
X R
X X X X
X X
X X
X −−( )− +
− − +( )
+ −× −
− −
12
7 26
7 21
5
4 7
3
3 12
2
2
X
X
X
X X
X
X
check:
XX
X X X
X X X
X X X
+
+ −
+ − ++
+ − +
21
4 7
19 215
19 26
3 2
3 2
3 2
X
X X X
X X
X
X
X
X
+× −
3
2 6
2
3 6
3 6
0
3
check:
22
2 6
3
6
3 5
2 5 11 10
2
2
2
3 2
− −
+
+ −
− +
− − + −
−
X
X X
X X
X X
X X X X
X
10.
33 2
2
2
2
3 11
3 6
5 10
5 10
0
−( )− +
− − +( )−
− −( )
X
X X
X X
X
X
X
check:22
2
3 2
3 2
3 52
2 6 10
3 5
5 11 10
− +× −
− + −
− +
− + −
XX
X X
X X X
X X X
X11. 22
3 2
3 2
2
2
4 7 5
3 19 26
3
4 19
4
+ −
− + − +
− −( )−
−
X R
X X X X
X X
X X
X −−( )− +
− − +( )
+ −× −
− −
12
7 26
7 21
5
4 7
3
3 12
2
2
X
X
X
X X
X
X
check:
XX
X X X
X X X
X X X
+
+ −
+ − ++
+ − +
21
4 7
19 215
19 26
3 2
3 2
3 2
Systematic Review 24CSystematicReview 23C1. 4 6 5
1 4 10 1
4
2
X R
X X X
+ −
+ + +
− XX X
X
X
XX
X
X X
X
2
2
2
4
6 1
6 6
5
4 61
4 6
4 6
4 10
+( )+
− +( )−
+× +
++
+
2.
XX
X X
X R
X
++ −( )
+ ++
+
6
5
4 10 1
2 2 3
2 1 4
2
3.
XX X
X X
X
X
XX
X
X
2
2
2
6 5
4 2
4 5
4 2
3
2 22 1
2 2
4
+ +
− +( )+
− +( )
+× +
+
4.
++
+ ++
+ ++
+ +
4
4 6 2
3
4 6 5
5
4
2
2
2
X
X X
X X
X
X X
5.
99 20
4
5 20
5 20
0
4
5
5 20
4
2
2
X
X X
X
X
X
X
X
X X
+
− +( )+
− +( )
+× +
+
+
6.
XX X
X X X
X
X
X
X X
X X
2
2
2
2
9 20
2 1 1
1
1
1
2 1
+ +
+ + = ++
× ++
+
+ +
7.
8.
9. XX Y Y Y X Y Y
X Y Y X Y
43
26
2 0 4 3 2 6 2 0
12 12 2 12 1
( ) ( ) ( )( ) = =
=
× × +
22 2 12 14
5
35 3 5 3 8
5 2 4 5
+
−+
− −
=
= = =
=
X Y
A
AA A A A
X X X X
aLGeBra 1
sYsteMatic reVieW 24c - sYsteMatic reVieW 24D
soLutions 257
99 20
4
5 20
5 20
0
4
5
5 20
4
2
2
X
X X
X
X
X
X
X
X X
+× +
+
+
6.
XX X
X X X
X
X
X
X X
X X
2
2
2
2
9 20
2 1 1
1
1
1
2 1
+ +
+ + = ++
× ++
+
+ +
7.
8.
9. XX Y Y Y X Y Y
X Y Y X Y
43
26
2 0 4 3 2 6 2 0
12 12 2 12 1
( ) ( ) ( )( ) = =
=
× × +
22 2 12 14
5
35 3 5 3 8
5 2 4 5
+
−+
− −
=
= = =
=
X Y
A
AA A A A
X X X X
10.
11. ÷ ++ −( )− −( ) =2 4 7X
12. 2 3 4
2 31
4
2
12
11 1
1 2
XY YY
XX Y
XY
Y XXY
X
− −
−− −
+ −( )
− + =
− + =
YYY X
XYXY
XY XY
XY XY
or
− + = − + =
− +
−31
4 2 3 4
4
1
, using commmon
denominators to add:
− + = −XXY XY
XXY
2 24 4
2313. . 44 21 04914
540 15 3600
7 9 63
4
× ==
−( ) −( ) =−
. .
.14.
15.
16.
÷
88 1 4 1 3 3
6 3 2
5 1
7 2 1
2
2
2
2
+ = − + = − =
− +
+ + −
+ +
17.
18.
X X
X X
X X
X ++ −
+ − −
−
4 8
4 9
2 17
97
2
2
X
X X
X
19. is prime, so 1 and 977
addition and multiplication20.
Systematic Review 24DSystematicReview 23D1. 2 3 13
1 2 10
2
2
X R
X X X
X
−
+ − +
− 22
2
2
2
3 10
3 3
13
2 3
1
2 3
2 3
2
+( )− +
− − −( )
−× +
−
−
−
X
X
X
X
X
X
X X
X
2.
XX
X X
X
X X X
X X
X
−+
− ++
+ + +
− +
3
13
2 10
3 2
3 3 11 6
3 9
2
2
2
2
1. 2 3 13
1 2 10
2
2
X R
X X X
X
−
+ − +
− 22
2
2
2
3 10
3 3
13
2 3
1
2 3
2 3
2
+( )− +
− − −( )
−× +
−
−
−
X
X
X
X
X
X
X X
X
2.
XX
X X
X
X X X
X X
X
−+
− ++
+ + +
− +( )+
3
13
2 10
3 2
3 3 11 6
3 9
2
2
2
2
3.
66
2 6
0
3 2
3
9 6
3 2
3 11 6
3 2
2
2
− +( )
+× +
+
+
+ +−
X
X
X
X
X X
X X
X R
4.
5. −
+ + −
− +( )− −
− − −( )−
−
1
4 3 10 9
3 12
2 9
2 8
1
3
2
2
X X X
X X
X
X
X6. 224
12 8
3 2
3 10 81
3 10 9
8 1
2
2
2
2
× +
−−
+ −−
+ −
+ +
X
X
X X
X X
X X
X X7. 66 4
44
4 16
4
8 16
2
2
5 7 32
4
= ++
× +
++
+ +
( )−
X
XX
X
X X
X X
A B B A
8.
9. (( ) = ( ) =
( ) = =
+−
−×− ×−
−
A B A
A B A A B A
A
5 7 32
4
5 102
4 5 2 10 2 4
10BB A A B
A B orA B
B
AB
B
− − + −
− −
−
= =
=
20 4 10 4 20
6 206 20
4
2
1
10.44 2 4 2 6
6 1
586 1 5 879
125
BA
BA
BA
or B A= =
× =
+ −
. . .11.
12. ÷22 5 50
7 9 16
10 2 8 5 8 3 3
7 4
. =−( ) − = −
− = − = − =
+
13.
14.
15.
aLGeBra 1
sYsteMatic reVieW 24D - sYsteMatic reVieW 24e
soLutions258
224
12 8
3 2
3 10 81
3 10 9
8 1
2
2
2
2
× +
−−
+ −−
+ −
+ +
X
X X
X X
X X
X X7. 66 4
44
4 16
4
8 16
2
2
5 7 32
4
= ++
× +
++
+ +
( )−
X
XX
X
X X
X X
A B B A
8.
9. (( ) = ( ) =
( ) = =
+−
−×− ×−
−
A B A
A B A A B A
A
5 7 32
4
5 102
4 5 2 10 2 4
10BB A A B
A B orA B
B
AB
B
− − + −
− −
−
= =
=
20 4 10 4 20
6 206 20
4
2
1
10.44 2 4 2 6
6 1
586 1 5 879
125
BA
BA
BA
or B A= =
× =
+ −
. . .11.
12. ÷22 5 50
7 9 16
10 2 8 5 8 3 3
7 42
. =−( ) − = −
− = − = − =
+
13.
14.
15.
÷
X X −−
+ − + +
+ +
+ +
+ − −
+
1
2 3 6
5 7 5
11 5
8 6
2 3
2
2
2
2
2
X X
X X
X X
X X
X
16.
XX −= × × × × ×
1
216 2 2 2 3 3 317.
18. addition and multiplicaation
19.
20.
24 6 4
24 3 8
÷
÷
==
hours
hours
Systematic Review 24ESystematicReview 23E1. X
X X X
X
+
+ + +− +
4
2 2 2 10 8
2 2
2
2 XX
X
X
X
X
X
X X
X X
( )+
− +( )
+× +
++
+ +
8 8
8 8
0
2 2
4
8 8
2 2
2 10 8
2
2
2.
3. 33 2
4 3 10 8
3 12
2 8
2 8
0
3
2
2
X
X X X
X X
X
X
X
−
+ + −
− +( )− −
− − −( )
−4. 224
12 8
3 2
3 10 8
2 4 3
2 5 4 2
2
2
2
× +
−−
+ −+
− −
X
X
X X
X X
X R
X X X
5.
−−
− −( )17
4 10
8 17
8 20
3
2 52 4
8 20
4
2.
3. 33 2
4 3 10 8
3 12
2 8
2 8
0
3
2
2
X
X X X
X X
X
X
X
−
+ + −
− +( )− −
− − −( )
−4. 224
12 8
3 2
3 10 8
2 4 3
2 5 4 2
2
2
2
× +
−−
+ −+
− −
X
X
X X
X X
X R
X X X
5.
−−
− −( )−
− −( )
−× +
−
17
4 10
8 17
8 20
3
2 52 4
8 20
4
2
2
X X
X
X
XX
X
X
6.
−−
− −+
− −
+ + = ++
× +
10
4 2 203
4 2 17
6 9 3
3
2
2
2
X
X X
X X
X X X
X
X
7.
8.
33
3 9
3
6 9
4 2
2 2 2
2
2
3
23
2 3 6
4
X
X X
X X
X Y
++
+ +
( ) =
( ) = =×
−
9.
10.
?
223
3 5 1
4 3 2 3
3 1 5
12 6
2 5
12
( )= = =
−
× − ×
+ −( )−
X Y X
X Y
X Y
X Y
X Y
X Y−− − − + −( ) − + −( )
−
= =6 2 5 12 2 6 5
10 1110
11
X Y X Y
X Y or X
Y
11. 110 10
10 10 10
4 1
4 1 4 14
( ) = ( )= = ( )×
?
12. 3 6 7
3 6 7
2 33 3
13 3
2 1 3 3 1 3 3 3
A B A A B
AB A
A B A A B B A
+ − =
+ − =
−
+
33 6 7
6 4
1 68 045 1
3 3 3 1 3 3 3
4 3 3 3
A B A B A B
A B A B
+ − =
−+ =
+
13. . . .7725
49 007 7 000
2 4 6
10
3 5
2
2
2
14.
15.
÷ =
+ −
+ + −
+ −
. ,
X X
X X
X X 116
5 11 3
4 5 7
6 4
132 2 2 3
2
2
2
16.
17.
X X
X X
X X
+ −
+ − − +
+ += × × ×111
2
18 9 2
18 3 6
aLGeBra 1
sYsteMatic reVieW 24e - Lesson Practice 25a
soLutions 259
3 6 7
3 6 7
2 33 3
13 3
2 1 3 3 1 3 3 3
A B A A B
AB A
A B A A B B A
+ − =
+ − =
−
+
33 6 7
6 4
1 68 045 1
3 3 3 1 3 3 3
4 3 3 3
A B A B A B
A B A B
+ − =
−+ =
+
13. . . .7725
49 007 7 000
2 4 6
10
3 5
2
2
2
14.
15.
÷ =
+ −
+ + −
+ −
. ,
X X
X X
X X 116
5 11 3
4 5 7
6 4
132 2 2 3
2
2
2
16.
17.
X X
X X
X X
+ −
+ − − +
+ += × × ×111
2
18 9 2
18 3 6
18.
19.
20.
X
hours
hours
÷ =÷ =
Lesson Practice 25A1. X X X
XX
X
X X
X
2
2
2
4 2 2
22
2 4
2
4
− = −( ) +( )+
× −
− −+
−
2. X X X
XX
X
X X
X
2
2
2
16 4 4
44
4 16
4
16
− = −( ) +( )+
× −
− −+
−
3. X X X
XX
X
X X
X
2
2
2
25 5 5
55
5 25
5
25
− = −( ) +( )+
× −
− −+
−
4. Y Y Y
YY
Y
Y Y
Y
2
2
2
144 12 12
1212
12 144
12
− = −( ) +( )+
× −
− −+
−1144
5. X X X
XX
X
X X
X
2
2
2
100 10 10
1010
10 100
10
− = −( ) +( )+
× −
− −+
−1100
6. X X X
XX
X
X X
X
2
2
2
81 9 9
99
9 81
9
81
− = −( ) +( )+
× −
− −+
−
7. X X X
XX
X
X X
X
2
2
2
49 7 7
77
7 49
7
49
− = −( ) +( )+
× −
− −+
−
8. X X X
XX
X
X X
X
2
2
2
64 8 8
88
8 64
8
64
− = −( ) +( )+
× −
− −+
−
9. A A A
AA
A
A A
A
2
2
2
121 11 11
1111
11 121
11
− = −( ) +( )+
× −
− −
−
−1121
10.
11.
X Y X Y X Y
X YX Y
XY Y
X XY
X Y
B
2 2
2
2
2 2
2
− = −( ) +( )+
× −
− −+
−
−− = −( ) +( )+
× −− −
+−
4 2 2
2
2
2 4
2
4
2
2
B B
B
B
B
B B
B
aLGeBra 1
Lesson Practice 25a - Lesson Practice 25B
soLutions260
10.
11.
X Y X Y X Y
X YX Y
XY Y
X XY
X Y
B
2 2
2
2
2 2
2
− = −( ) +( )+
× −
− −+
−
−− = −( ) +( )+
× −− −
+−
4 2 2
2
2
2 4
2
4
2
2
B B
B
B
B
B B
B
12. X X X
XX
X
X X
X
2
2
2
9 3 3
33
3 9
3
9
− = −( ) +( )+
× −
− −+
−
13.
14.
15.
16.
6565
4225
3535
1225
4842
2016
8585
722
×
×
×
×
55
13.
14.
15.
16.
6565
4225
3535
1225
4842
2016
8585
722
×
×
×
×
55
Lesson Practice 25BLessonPractice 24B1. X X X
XX
X
2 1 1 1
11
1
− = −( ) +( )+
× −
− −XX X
X
X X X
XX
X
X X
X
2
2
2
2
2
1
36 6 6
66
6 36
6
+
−
− = −( ) +( )+
× −
− −+
2.
−−36
LessonPractice 24B1. X X X
XX
X
2 1 1 1
11
1
− = −( ) +( )+
× −
− −XX X
X
X X X
XX
X
X X
X
2
2
2
2
2
1
36 6 6
66
6 36
6
+
−
− = −( ) +( )+
× −
− −+
2.
−−36
3.
4.
Y Y Y
YY
Y
Y Y
Y
A B
2
2
2
2
16 4 4
44
4 16
4
16
− = −( ) +( )+
× −
− −+
−
− 22
2
2
2 2
= −( ) +( )+
× −
− −+
−
A B A B
A BA B
AB B
A AB
A B
3.
4.
Y Y Y
YY
Y
Y Y
Y
A B
2
2
2
2
16 4 4
44
4 16
4
16
− = −( ) +( )+
× −
− −+
−
− 22
2
2
2 2
= −( ) +( )+
× −
− −+
−
A B A B
A BA B
AB B
A AB
A B
5.
6.
A A A
AA
A
A A
A
B
2
2
2
2
49 7 7
77
7 49
7
49
2
− = −( ) +( )+
× −
− −+
−
− 55 5 5
55
5 25
5
25
2
2
= −( ) +( )+
× −
− −+
−
B B
BB
B
B B
B
7.
8.
Y X Y X Y X
Y XY X
XY X
Y XY
Y X
X
2 2
2
2
2 2
2 4
− = −( ) +( )+
× −
− −+
−
− == −( ) +( )+
× −
− −+
−
X X
XX
X
X X
X
2 2
22
2 4
2
4
2
2
9. A A A
AA
A
A A
A
2
2
2
144 12 12
1212
12 144
12
− = −( ) +( )+
× −
− −+
−1144
4 4 4
4
2 2 2 210. X Y X Y
X Y X Y
X Y
X Y
− = ( ) −( ) =( ) −( ) +( )
+× −
− XXY Y
X XY
X Y
B B
X X
−
+−
−( ) +( )−( ) +( )
2
2
2 2
8 8
9 9
57
11.
12.
13.
aLGeBra 1
Lesson Practice 25B - sYsteMatic reVieW 25c
soLutions 261
9. A A A
AA
A
A A
A
2
2
2
144 12 12
1212
12 144
12
− = −( ) +( )+
× −
− −+
−1144
4 4 4
4
2 2 2 210. X Y X Y
X Y X Y
X Y
X Y
− = ( ) −( ) =( ) −( ) +( )
+× −
− XXY Y
X XY
X Y
B B
X X
−
+−
−( ) +( )−( ) +( )
2
2
2 2
8 8
9 9
57
11.
12.
13.553
3021
7575
5625
3535
1225
9694
9024
14.
15.
16.
Systematic Review 25C1.
2.
3.
X X X
XX
X
X X
X
X
2
2
2
2
16 4 4
44
4 16
4
16
− = −( ) +( )+
× −
− −+
−
−− = −( ) +( )+
× −
− −+
−+
36 6 6
66
6 36
6
36
2 5
2
2
X X
XX
X
X X
X
X
4.
5. RR
X X X
X X
X
X
XX
10
1 2 3 5
2 2
5 5
5 5
10
2 5
2
2
− + +
− −( )+
− −( )
+×
6.−−
− −+
+ −+
+ +
=
1
2 5
2 5
2 3 510
2 3 5
4 2
4 1
2
2
2
2
X
X X
X X
X X
X X
1.
2.
3.
X X X
XX
X
X X
X
X
+× −
− −+
−
−− = −( ) +( )+
× −
− −+
−+
36 6 6
66
6 36
6
36
2 5
2
2
X X
XX
X
X X
X
X
4.
5. RR
X X X
X X
X
X
XX
10
1 2 3 5
2 2
5 5
5 5
10
2 5
2
2
− + +
− −( )+
− −( )
+×
6.−−
− −+
+ −+
+ +
=
1
2 5
2 5
2 3 510
2 3 5
4 2
4 1
2
2
2
2
X
X X
X X
X X
X X7.
8. 00 400 20
45
2025
37
1221
2( ) = =
×
×
9.
10.
45
33
11.
12.
1
X X
X
X
X
X X
X X
−( ) −( )−
× −
− +
−
− +
7 11
7
11
11 77
7
18 77
2
2
33.
14.
2 2 2
2 3 6 0
2 3 6
32
3
55
5 5 25( ) = =− + == −
= −
×
Y X
Y X
Y X sl; oope
D X D X X
DX
=
+( ) +( ) = +( ) + +( ) =+
32
2 3 3 2 3
15.
16.
origin
33 2 6
300 000 000
1 000
300 000 000 000
D X
not
+ +
×17. , ,
,
$ , , , enough( )
+ =( ) =>− =( ) =>
+
18.
5 24 12 36
12 5 5 10
120Y X
Y X
Y 660 18060 60 120
180 300
30018053
5 5 10
XY X
Y
Y
Y
Y X
=− =
=
=
=
− = ==>
− =
− =
− =
− =
−
5 53
5 10
253
5 10
253
10 5
253
303
5
X
X
X
X
553
5
53
5
13
3 2 6
23
2
aLGeBra 1
sYsteMatic reVieW 25c - sYsteMatic reVieW 25D
soLutions262
Y X
Y X
Y X sl; oope
D X D X X
DX
=
+( ) +( ) = +( ) + +( ) =+
32
2 3 3 2 3
15.
16.
origin
33 2 6
300 000 000
1 000
300 000 000 000
D X
not
+ +
×17. , ,
,
$ , , , enough( )
+ =( ) =>− =( ) =>
+
18.
5 24 12 36
12 5 5 10
120Y X
Y X
Y 660 18060 60 120
180 300
30018053
5 5 10
XY X
Y
Y
Y
Y X
=− =
=
=
=
− = ==>
− =
− =
− =
− =
−
5 53
5 10
253
5 10
253
10 5
253
303
5
X
X
X
X
553
5
53
5
13
3 2 6
23
2
=
− =
= −
+
+
X
X
X
Y X
Y X
÷
≤
≤
19.
20.
see graph
YY X≤
≤
≤
≤
≤
23
2
4 23
3 2
4 63
2
4 2 2
4 0
+
−( ) −( ) +
− − +
− − +− true
origin
×X −11
−11X +77
X2 − 7X
X2 −18X +77
25( )5 = 25×5 = 225
2Y − 3X + 6 = 0
2Y = 3X − 6
Y = 32
X − 3;�slope = 32
D + 2( ) X +3( ) = D X +3( ) + 2 X +3( ) =DX +3D + 2X + 6
300,000,000
1,000
$300,000,000,000 not enough( )
5 24Y +12X = 36( ) ⇒120Y + 60X = 180
12 5Y −5X = 10( ) ⇒ 60Y − 60X = 120
180Y = 300
Y = 300180
= 53
3Y ≤ 2X + 6
Y ≤ 23
X + 2
see graph
Y
X
Systematic Review 25DSystematicReview 24D1.
2.
X X X
XX
2 4 2 2
22
− = −( ) +( )+
× −
−− −+
−
− = −( ) +( )+
× −
− −
2 4
2
4
25 5 5
55
5 2
2
2
2
X
X X
X
X X X
XX
X
3.
4.
55
5
25
2 3
2 2 7 6
2 43 63
2
2
2
2
X X
X
X
X X X
X XXX
+
−+
+ + +
− +( )+
− +
5.
66
0
2 3
2
4 6
2 3
2 7 6
10 25
2
2
2
( )
+× +
+
+
+ +
+ + = +
6.
7.
X
X
X
X X
X X
X X X 55
10 10 10 25 10 5
100 100 25 15
225 15
15
28. ( ) + ( ) + = ( ) +
+ + =
===
×
×
+ − = +( ) −(
15
6565
4225
7872
5616
3 4 4 12
9.
10.
11. X X X X ))+
× −
− −+
+ −
( ) =
( ) =
12.
13.
XX
X
X X
X X
41
4
4
3 4
49 7
7 7
2
2
3
23
2
?
×× =+ + == − −
= − −
= − −
3 67
4 8 2 0
4 8 2
84
24
2 12
14. Y X
Y X
Y X
Y X
slopee
A B C D E
A C D E B C D E
AC AD AE
SystematicReview 24D1.
2.
X X X
XX
2 4 2 2
22
− = −( ) +( )+
× −
−− −+
−
− = −( ) +( )+
× −
− −
2 4
2
4
25 5 5
55
5 2
2
2
2
X
X X
X
X X X
XX
X
3.
4.
55
5
25
2 3
2 2 7 6
2 43 63
2
2
2
2
X X
X
X
X X X
X XXX
+
−+
+ + +
− +( )+
− +
5.
66
0
2 3
2
4 6
2 3
2 7 6
10 25
2
2
2
( )
+× +
+
+
+ +
+ + = +
6.
7.
X
X
X
X X
X X
X X X 55
10 10 10 25 10 5
100 100 25 15
225 15
15
28. ( ) + ( ) + = ( ) +
+ + =
===
×
×
+ − = +( ) −(
15
6565
4225
7872
5616
3 4 4 12
9.
10.
11. X X X X ))+
× −
− −+
+ −
( ) =
( ) =
12.
13.
XX
X
X X
X X
41
4
4
3 4
49 7
7 7
2
2
3
23
2
?
×× =+ + == − −
= − −
= − −
3 67
4 8 2 0
4 8 2
84
24
2 12
14. Y X
Y X
Y X
Y X
slopee
A B C D E
A C D E B C D E
AC AD AE
aLGeBra 1
sYsteMatic reVieW 25D - sYsteMatic reVieW 25e
soLutions 263
+
+ + =
===
×
×
+ − = +( ) −(
15
6565
4225
7872
5616
3 4 4 12
9.
10.
11. X X X X ))+
× −
− −+
+ −
( ) =
( ) =
12.
13.
XX
X
X X
X X
41
4
4
3 4
49 7
7 7
2
2
3
23
2
?
×× =+ + == − −
= − −
= − −
3 67
4 8 2 0
4 8 2
84
24
2 12
14. Y X
Y X
Y X
Y X
slopee
A B C D E
A C D E B C D E
AC AD AE
= −+( ) + +( ) =+ +( ) + + +( ) =
+ +
2
15.
++ + +
×
BC BD BE
16. 300 000 00010 000
3 000 000 000 0
, ,,
$ , , , , 000
20 1
tan
mph hr
not enough( )17 -18. Rate Time Dis ce
220
10 2 20
5 4 20
4 5 20
1
mph hr
mph hr
mph hr
mi
mi
mi
mi
mmph hr
tan
mph hr
20 20
12 1 12
mi
Rate Time Dis ce19 - 20.
mph hr
mph hr
mph hr
mph
mi
mi
mi
mi
6 2 12
4 3 12
3 4 12
2 66 12
1 12 12
hr
mph hr
mi
mi
+
+ + =
===
×
×
+ − = +( ) −(
15
6565
4225
7872
5616
3 4 4 12
9.
10.
11. X X X X ))+
× −
− −+
+ −
( ) =
( ) =
12.
13.
XX
X
X X
X X
41
4
4
3 4
49 7
7 7
2
2
3
23
2
?
×× =+ + == − −
= − −
= − −
3 67
4 8 2 0
4 8 2
84
24
2 12
14. Y X
Y X
Y X
Y X
slopee
A B C D E
A C D E B C D E
AC AD AE
= −+( ) + +( ) =+ +( ) + + +( ) =
+ +
2
15.
++ + +
×
BC BD BE
16. 300 000 00010 000
3 000 000 000 0
, ,,
$ , , , , 000
20 1
tan
mph hr
not enough( )17 -18. Rate Time Dis ce
220
10 2 20
5 4 20
4 5 20
1
mph hr
mph hr
mph hr
mi
mi
mi
mi
mmph hr
tan
mph hr
20 20
12 1 12
mi
Rate Time Dis ce19 - 20.
mph hr
mph hr
mph hr
mph
mi
mi
mi
mi
6 2 12
4 3 12
3 4 12
2 66 12
1 12 12
hr
mph hr
mi
mi
+
+ + =
===
×
×
+ − = +( ) −(
15
6565
4225
7872
5616
3 4 4 12
9.
10.
11. X X X X ))+
× −
− −+
+ −
( ) =
( ) =
12.
13.
XX
X
X X
X X
41
4
4
3 4
49 7
7 7
2
2
3
23
2
?
×× =+ + == − −
= − −
= − −
3 67
4 8 2 0
4 8 2
84
24
2 12
14. Y X
Y X
Y X
Y X
slopee
A B C D E
A C D E B C D E
AC AD AE
= −+( ) + +( ) =+ +( ) + + +( ) =
+ +
2
15.
++ + +
×
BC BD BE
16. 300 000 00010 000
3 000 000 000 0
, ,,
$ , , , , 000
20 1
tan
mph hr
not enough( )17 -18. Rate Time Dis ce
220
10 2 20
5 4 20
4 5 20
1
mph hr
mph hr
mph hr
mi
mi
mi
mi
mmph hr
tan
mph hr
20 20
12 1 12
mi
Rate Time Dis ce19 - 20.
mph hr
mph hr
mph hr
mph
mi
mi
mi
mi
6 2 12
4 3 12
3 4 12
2 66 12
1 12 12
hr
mph hr
mi
mi
Systematic Review 25ESystematicReview 24E1.
2.
X X X
XX
2 9 3 3
33
− = −( ) +( )+
× −
−− −× +
−
− = −( ) +( )+
× −
− −
3 9
3
9
2
2
2 2
X
X X
X
X Y X Y X Y
X YX Y
XY
3.
4.
YY
X XY
X Y
X X R
X X X X
X X
2
2
2 2
2
3 2
3
+
−
+ −
+ + + −
− +
SystematicReview 24E1.
2.
X X X
XX
2 9 3 3
33
− = −( ) +( )+
× −
−− −× +
−
− = −( ) +( )+
× −
− −
3 9
3
9
2
2
2 2
X
X X
X
X Y X Y X Y
X YX Y
XY
3.
4.
YY
X XY
X Y
X X R
X X X X
X X
2
2
2 2
2
3 2
3
2 8
4 2 9 4 8
2 8
+
−
+ −
+ + + −
− +
5.
22
2
2
2
2
3 2
3
4
4
8
24
8 4
2
2 9
( )+
− +( )−
+× +
+
+
+
X X
X X
X XX
X X
X X
X
6.
XX X
X X X
X X X
2
3 2
2
2
4
8
2 9 4 8
4 4 1 2 1
4 10 4 10
+−
+ + −
+ + = +
( ) +
7.
8. (( ) + = ( ) +( ) + + = +
==
×
1 2 10 1
4 100 40 1 20 1
441 21
21 21
8585
9.
77225
5951
3009
10 24 6 4
6
2
10.
11.
12.
×
− + = −( ) −( )−
×
X X X X
XXX
X
X X
X X
Q R X Y Q X Y R X
−
− +−
− ++( ) +( ) = +( ) +
4
4 24
6
10 24
2
2
13. ++( ) =+ + +
Y
QX QY RX RY
14. $ , , , ,, ,
5 000 000 000 000300 000 0000
50 0003
16 666 67
5 000 000 000 000
=
×
$ ,
$ , .
$ , , , ,
.
≈
15.
aLGeBra 1
sYsteMatic reVieW 25e - Lesson Practice 26B
soLutions264
+ + = +
==
×
1 2 10 1
4 100 40 1 20 1
441 21
21 21
8585
77225
5951
3009
10 24 6 4
6
2
10.
11.
12.
×
− + = −( ) −( )−
×
X X X X
XXX
X
X X
X X
Q R X Y Q X Y R X
−
− +−
− ++( ) +( ) = +( ) +
4
4 24
6
10 24
2
2
13. ++( ) =+ + +
Y
QX QY RX RY
14. $ , , , ,, ,
5 000 000 000 000300 000 0000
50 0003
16 666 67
5 000 000 000 000
=
×
$ ,
$ , .
$ , , , ,
.
≈
15.
008
400 000 000 000 00
400
$ , , , .
$ billion in interest eeach year
16.
17.
18.
300 50 6
300 60 5
÷
÷
==
hours
hours
66 5 46 299
46 8 54
299 54 5 54
.
mph
.
× =+ =
miles
hour
19.
÷ ≈ ss
R R R XRR R XR
R XRR
RX
20. 4 32 36 828 36 8
64 8648
− = +− − =
− =− = == −8
Lesson Practice 26ALessonPractice 25A1.
2.
X X X
X Y X
4 2 2
4 4
9 3 3− = −( ) +( )− = 22 2 2 2
2 2
3 22 16 2
−( ) +( ) =−( ) +( ) +( )− = −
Y X Y
X Y X Y X Y
X X X X3. 888 4 4 2 4 2
2 2 4 2
( )− = −( ) +( ) =−( ) +( ) +( )
4.
5
X Y X Y X Y
X Y X Y X Y
..
6.
2 10 12 2 5 6
2 2 3
5 5
3 2 2
3
X X X X X X
X X X
X X
+ + = + +( ) =+( ) +( )
+ 22 2
3 2
30 5 6
5 3 2
2 11 5 2
− = + −( ) =+( ) −( )
+ + =
X X X X
X X X
X X X X X7. 22
2
3
11 5
2 1 5
3 12 3 4
2 1
+ +( ) =+( ) +( )
− = −( )−
X
X X X
X X X X
X
8.
9. 88 2 9
2 3 3
5 20 25
5
2
4 3 2
2 2
X X X
X X X
X X X
X X
= −( ) =−( ) +( )
− − =10.
−− −( ) = −( ) +( )+ − =
+ −
4 5 5 5 1
4 16 48
4 4 1
2
3 2
2
X X X X
X X X
X X X
11.
22 4 6 2
2 32 2 16
2 4 4
4 4
2 2
( ) = +( ) −( )− = −( ) =−( ) +
X X X
X X
X X
12.
(( ) = −( ) +( ) +( )2 2 2 4
5 4 5 4
2
3 2 2
X X X
X X X X X X
X X
..
6.
2 10 12 2 5 6
2 2 3
5 5
3 2 2
3
X X X X X X
X X X
X X
=+( ) +( )
+ 22 2
3 2
30 5 6
5 3 2
2 11 5 2
− = + −( ) =+( ) −( )
+ + =
X X X X
X X X
X X X X X7. 22
2
3
11 5
2 1 5
3 12 3 4
2 1
+ +( ) =+( ) +( )
− = −( )−
X
X X X
X X X X
X
8.
9. 88 2 9
2 3 3
5 20 25
5
2
4 3 2
2 2
X X X
X X X
X X X
X X
= −( ) =−( ) +( )
− − =10.
−− −( ) = −( ) +( )+ − =
+ −
4 5 5 5 1
4 16 48
4 4 1
2
3 2
2
X X X X
X X X
X X X
11.
22 4 6 2
2 32 2 16
2 4 4
4 4
2 2
( ) = +( ) −( )− = −( ) =−( ) +
X X X
X X
X X
12.
(( ) = −( ) +( ) +( )+ + = + +( ) =
2 2 2 4
5 4 5 4
2
3 2 2
X X X
X X X X X X
X X
13.
++( ) +( )+ − = + −( ) =+( ) −(
4 1
3 6 9 3 2 3
3 3 1
3 2 2
X
X X X X X X
X X X
14.))
+ − = + −( ) =−( ) +( )
−
15.
16.
2 7 4 2 7 4
2 1 4
4
3 2 2
3
X X X X X X
X X X
X 116 4 4
4 2 2
2X X X
X X X
= −( ) =−( ) +( )
Lesson Practice 26BLessonPractice 25B1. X X X X
X X X
4 2 2 2
2
9 9
3 3
− = −( ) =−( ) +(( )
− = −( ) =−( ) +( )
− =
2.
3.
3 75 3 25
3 5 5
4 4 4
3 2
4 2
X X X X
X X X
X X X22 2
2
5 4
2
1
4 1 1
5 5 5 1
5 1
X
X X X
X X X X
X X
−( ) =−( ) +( )
− = −( ) =−(
4.
)) +( ) =−( ) +( ) +( )
− − − = − +
X
X X X X
X X X
2
2
2 2
1
5 1 1 1
2 16 30 2 85. XX
X X
X X X X X X
+( ) =− +( ) +( )
+ − = + −( ) =
15
2 5 3
3 9 30 3 3 103 2 26.
33 5 2
5 5 30 5 6
5 3
3 2 2
X X X
X X X X X X
X X X
+( ) −( )− − = − −( ) =−( ) +
7.
22
11 30 11 30
6 5
4
3 2 2
( )+ + = + +( ) =+( ) +( )
−
8.
9.
X X X X X X
X X X
X22 2
3 2
28 40 4 7 10
4 2 5
3 24
− − = − + +( ) =− +( ) +( )− −
X X X
X X
X X10. −− =
− + +( ) = − +( ) +( )− −
36
3 8 12 3 2 6
2 8 10
2
3 2
X
X X X X X X
X X X11. == − −( ) =−( ) +( )
− − = −
2 4 5
2 5 1
5 6 5
2
5 4 3 3 2
X X X
X X X
X X X X X X12. −−( ) =−( ) +( )
− − + =
− + −
6
5 6 1
3 12 36
3 4 12
3
3 2
2
X X X
X X X
X X X
13.
(( )
aLGeBra 1
Lesson Practice 26B - sYsteMatic reVieW 26c
soLutions 265
33 5 2
5 5 30 5 6
5 3
X X X
X X X X X X
X X X
− − = − −( ) =−( ) +
7.
22
11 30 11 30
6 5
4
3 2 2
( )+ + = + +( ) =+( ) +( )
−
8.
9.
X X X X X X
X X X
X22 2
3 2
28 40 4 7 10
4 2 5
3 24
− − = − + +( ) =− +( ) +( )− −
X X X
X X
X X10. −− =
− + +( ) = − +( ) +( )− −
36
3 8 12 3 2 6
2 8 10
2
3 2
X
X X X X X X
X X X11. == − −( ) =−( ) +( )
− − = −
2 4 5
2 5 1
5 6 5
2
5 4 3 3 2
X X X
X X X
X X X X X X12. −−( ) =−( ) +( )
− − + =
− + −
6
5 6 1
3 12 36
3 4 12
3
3 2
2
X X X
X X X
X X X
13.
(( ) = − +( ) −( )+ − = + −( ) =
+
3 6 2
3 4 3 44 3 2 2 2
2
X X X
X X X X X X
X X
14.
44 1
4 36 4 9
4 3 3
2
3 2
4
( ) −( )− = −( ) =−( ) +( )
X
X X X X
X X X
X
15.
16. −− = −( ) =−( ) +( )
32 2 16
2 4 4
2 2 2
2
X X X
X X X
Systematic Review 26C1.
2.
X X X
X X X
4 2 2
2
4
16 4 4
2 2 4
10 16
− = −( ) +( ) =−( ) +( ) +( )( ) − == ( ) −( ) ( ) +( ) ( ) +( )
− = ( )( )10 2 10 2 10 4
10 000 16 8 12 100
2
, ++( )( )= ( )( )=
− = −(
4
9 984 96 104
9 984 9 984
16 9 4 32
,
, ,
3. X X )) +( )
( ) − = ( ) −( ) ( ) +( )( ) −
4 3
16 10 9 4 10 3 4 10 3
16 100 9
2
X
4.
== −( ) +( )− = ( )( )
=
40 3 40 3
1 600 9 37 43
1 591 1 591
,
, ,
5.
6
3 8 7
2 3 2 9
3 6
8 9
8 16
7
2
2
X R
X X X
X X
X
X
−
+ − −
− +( )− −
− − −( )
..
7.
3 8
2
6 16
3 8
3 2 167
3 2 9
3
2
2
2
X
X
X
X X
X X
X X
X
−× +
−
−
− −+
− −
−( ) XX X X
X
X
X
X X
X X
−( ) = − +−
× −− +
−
− +
4 7 12
3
4
4 12
3
7 12
2
2
2
8.
5.
6
3 8 7
2 3 2 9
3 6
8 9
8 16
7
2
2
X R
X X X
X X
X
X
−
+ − −
− +( )− −
− − −( )
..
7.
3 8
2
6 16
3 8
3 2 167
3 2 9
3
2
2
2
X
X
X
X X
X X
X X
X
−× +
−
−
− −+
− −
−( ) XX X X
X
X
X
X X
X X
−( ) = − +−
× −− +
−
− +
4 7 12
3
4
4 12
3
7 12
2
2
2
8.
X − 3( )
X − 4( )
5.
6
3 8 7
2 3 2 9
3 6
8 9
8 16
7
2
2
X R
X X X
X X
X
X
−
+ − −
− +( )− −
− − −( )
..
7.
3 8
2
6 16
3 8
3 2 167
3 2 9
3
2
2
2
X
X
X
X X
X X
X X
X
−× +
−
−
− −+
− −
−( ) XX X X
X
X
X
X X
X X
−( ) = − +−
× −− +
−
− +
4 7 12
3
4
4 12
3
7 12
2
2
2
8.
9.
10.
11.
7575
5625
4149
2009
2 4 2 2 2 1
2
2 2
×
×
+ + = + +( ) =X X X X
XX X
XX
X
X X
X X
X X X
+( ) +( )+
× +
++
+ +
+ +( ) = +
1 1
11
1
2 1
2 2 1 2
2
2
2 2 44 2
6 600 6 100
6 10 10
101
2 2
X
X X
X X
XX
+
− = −( ) =−( ) +( )
+× −
12.
00
10 100
10
100
6 100 6 600
2
2
2 2
− −+
−
−( ) = −
X
X X
X
X X
aLGeBra 1
sYsteMatic reVieW 26c - sYsteMatic reVieW 26D
soLutions266
13. 37
6
37 1
61
37
61
37
71
61
71
3 42
423
=
× = ×
=
× = ×
=
=
Q
Q
Q
Q
Q
Q ==
=
× = ×
= =
= −
14
29 36
29
361 36
361
729
8
015 25
14.
15.
X
X
X
Q. . ..
. . .
44
1000 015 1000 25 44
15 250 440
15 440
( ) = −( )= −
+ =
Q
Q
2250
455 250
455250
1 82
4 16 5 434 5
Q
Q
Q
X XX
=
= =
− − = − +− +
.
16.XXX= +=
= × + × + × + ×
43 1659
49 703 4 10 9 10 7 10 3 104 3 2 017.
18
,
..
19.
1 10 5 10
01 0005 0105
12 1 4
2 4× + × =+ =
+( ) + ( ) =
− −
. . .
N N 99 2 812 12 4 9 18 812 4 9 18 8 12
7 1
NN N NN N N
N
+( ) ++ + = + ++ − = + −
= 44
147
2
2 3 4
2 3 4
2 4 3 4
N
X A
X A A
= =
+( ) +( ) =( ) +( ) + +( )
; ;
20.
== + + +2 8 3 12XA X A
Systematic Review 26DSystematicReview 25D1. X X X X X X X3 29 9 3 3− = −( ) = −( ) +( ))
( ) − ( ) = ( ) ( ) −( ) ( ) +( )− = (
2. 10 9 10 10 10 3 10 3
1000 90 10
3
))( )( )=
− = −( ) +( ) =−( ) +( )
7 13
910 910
81 9 9
3 3
4 2 23. X X X
X X XX2
4 2
9
10 81 10 3 10 3 10 9
10 0
+( )
( ) − = ( ) −( ) ( ) +( ) ( ) +( )4.
, 000 81 7 13 100 9
9 919 7 13 109
9 919 9
− = ( )( ) +( )= ( )( )( )=
,
, ,9919
5. 2 1 11
3 2 7 8
2 6
83
11
2
2
X R
X X X
X X
XX
− −
− − −
− −( )− −
− − +( )−
6.
7.
2 13
6 3
2
11
2 7 8
2 1
2
2
2
XX
X
X X
X X
X X X
−× −
− +−
−
− −
−( ) −( ) = −− +−
× −
− +−
− +
3 2
21
2
2
3 2
2
2
X
XX
X
X X
X X
8.
6.
7.
2 13
6 3
2
11
2 7 8
2 1
2
2
2
XX
X
X X
X X
X X X
−× −
− +−
−
− −
−( ) −( ) = −− +−
× −
− +−
− +
3 2
21
2
2
3 2
2
2
X
XX
X
X X
X X
8.
X − 2( )
X − 1( )
9.
10.
11.
9595
9025
2426
624
5X 45 5 X 9
5 X 3 X 3
2 2( )( ) ( )
×
×
− = − =− +
aLGeBra 1
sYsteMatic reVieW 26D - sYsteMatic reVieW 26e
soLutions 267
12.
13.
14.
4X 324
4 X 81
4 X 9 X 9
411
P110
4 110 11P440 11P44011
P 40
58
C15
5 15 8C75 8C758
C 9 38
2
2( )( ) ( )
−
−+ −
=
× ==
= =
=
× ==
= =
15. − + = −
−
50 30 80 40
5
BY B BY B
divide all terms by 10B:
YY Y
Y Y
Y
Y
+ = −+ = +
=
=
3 8 4
3 4 8 5
7 13
713
16. 2 07 9 5 83
100 2 07 9 100 5 83
207
. . .
. . .
− = +−( ) = +( )−
X X
X X
990 500 83207 83 500 90
124 590124590
622
X XX XX
X
= +− = +
=
= =995
17.
. . .25 10 2 30 100
14 10
25 10Q D
Q D
Q+ =( )( ) =>+ =( ) −( ) =>
+ DD
Q D
Q
Q
Q
Q D
=− − = −
=
=
=
+ = => ( )
230
10 10 140
15 90
90156
14 6 ++ == −=
D
DD
14
14 68
18.
19.
4 2 180 756
180 30 150
756 150 5
.
mph
.
× =− =
=
miles
÷ 004 hours
X A C B
X C B A C B
20. +( ) +( ) =( ) +( ) + ( ) +( )
Systematic Review 26E 1.
2.
3.
4.
X 25X X X 25
X X 5 X 5
10 25 10 10 10 5 10 5
10,000 25 100 100 5 15
10,000 2,500 7,500
7,500 7,500
5X 45X 5X X 9
5X X 3 X 3
5 10 45 10 5 10 10 3 10 3
5 1000 450 50 7 13
5,000 450 4,550
4,550 4,550
4 2 2 2
2
4 2 2
3 2
3
( )
( )
( )( )
( )( )
( ) ( )
( ) ( ) ( ) ( ) ( )( ) ( ) ( )
( ) ( )
( ) ( ) ( ) ( ) ( )( ) ( )( )
− = − =
− +
− = − +− =
− ==
− = − =− +
− = − +− =− =
=5. 2 7 29
4 2 2 1
2 2 8
7 1
7 28
29
X R
X X X
X X
X
X
−
+ + +
− +( )− +
− − −( )
66. 2 74
8 28
2 2 7
2 2 2829
2 2 1
XX
X
X X
X X
X X
−× +
−
−
+ −+
+ +
5. 2 7 29
4 2 2 1
2 2 8
7 1
7 28
29
X R
X X X
X X
X
X
−
+ + +
− +( )− +
− − −( )
66. 2 74
8 28
2 2 7
2 2 2829
2 2 1
XX
X
X X
X X
X X
−× +
−
−
+ −+
+ +
7.
8.
2 3 2 2 7 6
2 32
4 6
2 3
2
2
2
2
X X X X
XX
X
X X
X
−( ) −( ) = − +−
× −
− +−
−77 6
2525
625
3238
1216
1272 8
12 8 7296
X
A
A
+
×
×
=
× =
9.
10.
11.
==
= =
729672
1 13
A
A
X4 − 25X2 = X2 X2 − 25( ) =X2 X −5( ) X +5( )
10( )4 − 25 10( )2 = 10( )2 10( ) −5( ) 10( ) +5( )10,000 − 25 100( ) = 100 5( ) 15( )10,000 − 2,500 = 7,500
7,500 = 7,500
5X3 − 45X = 5X X2 − 9( ) =5X X −3( ) X +3( )
5 10( )3 − 45 10( ) = 5 10( ) 10( ) −3( ) 10( ) +3( )5 1000( ) − 450 = 50 7( ) 13( )5,000 − 450 = 4,550
4,550 = 4,550
2X − 7�R�29
X + 4�2X2 + X + 1
− 2X2 + 8X( )−7X + 1
− −7X − 28( )29
2X − 7
× X + 4
8X − 28
2X2 − 7X
2X2 + X − 28
+� 29
2X2 + X + 1
25
×25
625
32
× 38
1216
1272
= A8
12
2X −3( )
X −2( )
7.
8.
2 3 2 2 7 6
2 32
4 6
2 3
2
2
2
2
X X X X
XX
X
X X
X
−( ) −( ) = − +−
× −
− +−
−77 6
2525
625
3238
1216
1272 8
12 8 7296
X
A
A
+
×
×
=
× =
9.
10.
11.
aLGeBra 1
sYsteMatic reVieW 26e - Lesson Practice 27a
soLutions268
7.
8.
2 3 2 2 7 6
2 32
4 6
2 3
2
2
2
2
X X X X
XX
X
X X
X
−( ) −( ) = − +−
× −
− +−
−77 6
2525
625
3238
1216
1272 8
12 8 7296
X
A
A
+
×
×
=
× =
9.
10.
11.
==
= =
729672
1 13
A
A
12. 512
20
5 12 205 240
2405
48
=
= ×=
= =
YYY
Y
13. − + =− +( ) = ( )
− +
. . .
. . .
35 55 2 2
100 35 55 100 2 2
35 5
Y Y
Y Y
Y 55 22020 220
22020
11
100 1
1100
0
YY
Y
WF
WF
==
= =
× =
=
14.
15. . 3378 3 10 7 10 8 10
2 10 6 10 1 10
2
2 3 4
6 4 3
= × + × + ×
× + × + × =
− − −
16.
,, , , ,
, ,
000 000 60 000 1 000
2 061 000
2 2 2
+ + =
( ) + +( ) −17. N N 55 7 42 2 4 5 7 4
2 2 7 4 4 53 12
= + +( )+ + − = + +
+ − = + − +=
=
NN N N
N N NN
N 1123
4
4 6 8
442 52 8 5
212 1 212
=
=× =
; ;
.18.
19.
÷ hours
milles
X X X X X
X X X
20. 3 2 3 3 3 2 3
3 9 2 62
+( ) +( ) = +( ) + +( ) =+( ) + +(( )
Lesson Practice 27A LessonPractice 26A1.
2.
X X
X X
X
2 2 15 0
5 3 0
− − =−( ) +( ) =−55 0
53 0
3
5 2 5 15 0
25 10 15 00 0
3
2
==
+ == −
( ) − ( ) − =− − =
=
−
XX
X
3.
(( ) − −( ) − =+ − =
=
− + =
− +
2
3 2
2
2 3 15 0
9 6 15 00 0
3 2 0
3 2
4. X X X
X X X(( ) =−( ) −( ) =
= − ==
− ==
( ) −
0
2 1 0
0 2 02
1 01
0 33
X X X
X XX
XX
5.
6. 00 2 0 0
0 0 0 00 0
2 3 2 2 2 0
8 3 4 2
2
3 2
( ) + ( ) =+ + =
=
( ) − ( ) + ( ) =− ( ) + 22 0
8 12 4 00 0
1 3 1 2 1 01 3 2 0
0 0
3 2
( ) =− + =
=
( ) − ( ) + ( ) =− + =
=
7.
8.
X X
X X
X X X
X XX
X
3
2
0
1 0
1 1 0
0 1 01
1
− =
−( ) =−( ) +( ) =
= − ==
+ = 001
0 0 0
0 0
1 1 01 1 0
0 0
1 1
3 3
3
X = −
( ) − ( ) ==
( ) − ( ) =− =
=
−( ) − −
9.
(( ) =− − −( ) =
=
− + =−( ) −( ) =
0
1 1 00 0
2 7 3 0
2 1 3 0
2
210.
11.
X X
X X
XXX
X
XX
− ==
=
− ==
−
+
1 02 1
12
3 03
2 12
7 12
32
12. ==
− + =
− + =
− + =
− + ==
0
2 14
72
3 0
12
72
3 0
62
3 0
3 3 00 0
2 3
aLGeBra 1
Lesson Practice 27a - sYsteMatic reVieW 27c
soLutions 269
001
0 0 0
0 0
1 1 01 1 0
0 0
1 1
3 3
3
=− =
=
−( ) − −(( ) =− − −( ) =
=
− + =−( ) −( ) =
0
1 1 00 0
2 7 3 0
2 1 3 0
2
210.
11.
X X
X X
XXX
X
XX
− ==
=
− ==
−
+
1 02 1
12
3 03
2 12
7 12
32
12. ==
− + =
− + =
− + =
− + ==
(
0
2 14
72
3 0
12
72
3 0
62
3 0
3 3 00 0
2 3)) − ( ) + =( ) − + =
− + ==
27 3 3 0
2 9 21 3 0
18 21 3 00 0
Lesson Practice 27B1.
2.
X X
X X
X X
XX
XX
2
2
56
56 0
7 8 0
8 08
7 0
+ =+ − =
−( ) +( ) =+ =
= −− =
== 7
3. −( ) + −( ) =− =
=
( ) + ( ) =+ =
8 8 56
64 8 5656 56
7 7 5649 7 56
56
2 2
==
− + =−( ) −( ) =
− ==
− ==
56
11 30 0
5 6 0
5 05
6 06
24.
5.
X X
X X
XX
XX
66. 5 11 5 30 0
25 55 30 00 0
6 11 6 30 0
3
2
2
( ) − ( ) + =− + =
=
( ) − ( ) + =66 66 30 0
0 0
15 56 0
7 8 0
7 0
2
− + ==
− + =−( ) −( ) =− =
=
7.
8.
X X
X X
XX 77
8 08
7 15 7 56 049 105 56 0
0 0
8 1
2
2
XX
− ==
( ) − ( ) + =− + =
=
( ) −
9.
55 8 56 0
64 120 56 00 0
13 40 0
5 8
( ) + =− + =
=
− + =−
5 11 5 30 0
25 55 30 00 0
6 11 6 30 0
3
2
2
+ =− + =
=
( ) − ( ) + =66 66 30 0
0 0
15 56 0
7 8 0
7 0
2
− + ==
− + =−( ) −( ) =− =
=
7.
8.
X X
X X
XX 77
8 08
7 15 7 56 049 105 56 0
0 0
8 1
2
2
XX
− ==
( ) − ( ) + =− + =
=
( ) −
9.
55 8 56 0
64 120 56 00 0
13 40 0
5 8
2
( ) + =− + =
=
− + =−( ) −(
10. X X
X X )) =− =
=− =
=
( ) − ( ) + =− +
0
5 05
8 08
5 13 5 40 0
25 65
2
11.
12.
XX
XX
440 00 0
8 13 8 40 0
64 104 40 00 0
2
==
( ) − ( ) + =− + =
=
Systematic Review 27CSystematicReview 26C1. 2 7 6 0
2 3 2 0
2
2X X
X X
+ + =+( ) +( ) =
XXX
X
XX
+ == −
= −
+ == −
− + −
3 02 3
32
2 02
2 32
7 32
2
2. + =
+ −
+ =
− + =
=
6 0
2 94
212
6 0
184
212
122
0
0 0
22 2 7 2 6 0
2 4 14 6 08 14 6 0
0 0
2−( ) + −( ) + =
( ) − + =− + =
=
aLGeBra 1
sYsteMatic reVieW 27c - sYsteMatic reVieW 27D
soLutions270
3.
4.
X X
X X
XX
XX
2 6 8 0
2 4 0
2 02
4 04
2
+ + =+( ) +( ) =+ =
= −+ =
= −
−( )22
2
6 2 8 04 12 8 0
0 0
4 6 4 8 016 24 8 0
+ −( ) + =− + =
=
−( ) + −( ) + =− + =
55. X X
X X
X X
X X
2
2
2
3 4 14
3 4 14 0
3 10 0
5 2 0
+ + =+ + − =
+ − =+( ) −( ) =
XXX
XX
+ == −
− ==
−( ) + −( ) + =− + =
5 05
2 02
5 3 5 4 14
25 15 4 141
26.
44 14
2 3 2 4 144 6 4 14
14 14
2
=
( ) + ( ) + =+ + =
=
7. X X X X−( ) −( ) = − +6 6 12 362
4.
5.
6.
7.
9.
10.
11.
12.
13.
14.
0
X + 2( ) X + 4( ) = 0
X + 2 = 0
X = −2
X + 4 = 0
X = −4
−2( )2 + 6 −2( ) + 8 = 0
4 − 12 + 8 = 0
0 = 0
−4( )2 + 6 −4( ) + 8 = 0
16 − 24 + 8 = 0
X2 + 3X + 4 = 14
X2 + 3X + 4 − 14 = 0
X2 + 3X − 10 = 0
X + 5( ) X − 2( ) = 0
X + 5 = 0
X = −5
X − 2 = 0
X = 2
−5( )2 + 3 −5( ) + 4 = 14
25 − 15 + 4 = 14
14 = 14
2( )2 + 3 2( ) + 4 = 14
4 + 6 + 4 = 14
14 = 14
X − 6
×X − 6
− 6X +36
X2 − 6X
X2 −12X + 36
X2 −16 = X − 4( ) X + 4( )
X2 − 49 = X −7( ) X +7( )
−42 + −2( )2 = − 4 × 4( ) + −2( ) −2( ) =−16 + 4 = −12
3−1 ×31 = 3−1+1 = 30 = 1
X2( )2 X−3( )−1 = X2×2X−3×−1 =
X4X3 = X4+3 = X7
2X2X−1YY3
− 3X0Y3
X2+ 5Y−2
X−1=
2X2X−1Y1Y−3 −3X0Y3X−2 +5Y−2X1 =
X −6( )
X −6( )
8.
9.
X
X
X
X X
X X
X X X
−× −
− +
−
− +
− = −( ) +( )
6
6
6 36
6
12 36
16 4 4
2
2
2
110.
11.
X X X2
2 2
49 7 7
4 2 4 4 2 2
− = −( ) +( )
− + −( ) = − ×( ) + −( ) −( )) =− + = −
× = = =
( ) ( )− − +
−−
16 4 12
3 3 3 3 11 1 1 1 0
22
31
12.
13. X X == =
= =
− +
× − ×−
+
−
X X
X X X X
X X Y
Y
X Y
X
2 2 3 1
4 3 4 3 7
2 1
3
0 3
22 3 514. YY
X
X X Y Y X Y X Y X
X Y
−
−
− − − −
+ −( ) +
= − +
=
2
1
2 1 1 3 0 3 2 2 1
2 1 1
2 3 5
2 −−( ) + −( ) −
− − −
−
− +
= − +
=
3 0 2 3 2
2 2 3 2
2
3 5
2 3 5
7
X Y XY
XY X Y XY
XY
8.
9.
X
X
X
X X
X X
X X X
−× −
− +
−
− +
− = −( ) +( )
6
6
6 36
6
12 36
16 4 4
2
2
2
110.
11.
X X X2
2 2
49 7 7
4 2 4 4 2 2
− = −( ) +( )
− + −( ) = − ×( ) + −( ) −( )) =− + = −
× = = =
( ) ( )− − +
−−
16 4 12
3 3 3 3 11 1 1 1 0
22
31
12.
13. X X == =
= =
− +
× − ×−
+
−
X X
X X X X
X X Y
Y
X Y
X
2 2 3 1
4 3 4 3 7
2 1
3
0 3
22 3 514. YY
X
X X Y Y X Y X Y X
X Y
−
−
− − − −
+ −( ) +
= − +
=
2
1
2 1 1 3 0 3 2 2 1
2 1 1
2 3 5
2 −−( ) + −( ) −
− − −
−
− +
= − +
=
3 0 2 3 2
2 2 3 2
2
3 5
2 3 5
7
X Y XY
XY X Y XY
XY −− −
+ − == − +
= −
−3 7 3
2 4 8 04 2 8
24
2 32
3
2X Y or X
Y
Y
X
X YY X
Y
15.
XX
Y X
+
= − +
2
12
2
16.
17.
18.
m = ( )
= × × ×
2
11
100 2 2 5 5
negative reciprocal
119.Y X
Y X
Y XX
X
Y X
= −( ) −( ) =>= −
− = − += − +=
= − =>
2 4 13
2 40 1
1
3 YYY
X X
X X
= ( ) −= −
−( )+( ) +( ) =
( ) +( ) + (
1 32
1 2
2 3 2 1
2 2 1 3
,
20.
)) +( ) =+( ) + +( )
2 1
4 2 6 32
X
X X X
Systematic Review 27DSystematicReview 26D1. 2 9 4 0
2 1 4 0
2
2X X
X X
+ + =+( ) +( ) =
XXX
X
XX
+ == −
= −
+ == −
− + −
1 02 1
12
4 04
2 12
9 12
2
2. + =
− + =
− + =
− + =
=
4 0
2 14
92
82
0
24
92
82
0
12
92
82
0
0 0
22 4 9 4 4 0
2 16 36 4 0
32 36 4 00 0
1
2
2
−( ) + −( ) + =( ) − + =
− + ==
+
aLGeBra 1
sYsteMatic reVieW 27D - sYsteMatic reVieW 27D
soLutions 271
1. 2 9 4 0
2 1 4 0
2
2X X
X X
+ + =+( ) +( ) =
XXX
X
XX
+ == −
= −
+ == −
− + −
1 02 1
12
4 04
2 12
9 12
2
2. + =
− + =
− + =
− + =
=
4 0
2 14
92
82
0
24
92
82
0
12
92
82
0
0 0
22 4 9 4 4 0
2 16 36 4 0
32 36 4 00 0
1
2
2
−( ) + −( ) + =( ) − + =
− + ==
+3. X 33 68 0
17 4 0
17 017
4 04
X
X X
XX
XX
− =+( ) −( ) =+ =
= −− =
=
4. −( ) + −( ) − =− − =
=
( ) + ( ) −
17 13 17 68 0289 221 68 0
0 0
4 13 4
2
2668 0
16 52 68 00 0
2 5 8
2 5 8 0
2 3
2
2
2
=+ − =
=
− + =− + − =
− −
5. X X
X X
X X ==−( ) +( ) =
− ==
+ == −
( ) − ( ) + =
0
3 1 0
3 03
1 01
3 2 3 5 82
X X
XX
XX
6.
99 6 5 88 8
1 2 1 5 81 2 5 8
8 8
2
− + ==
−( ) − −( ) + =+ + =
=
7. X X X X2 8 16 4 4− + = −( ) −( )
3.
4.
5.
6.
7.
8.
9.
0
2 14⎛⎝⎜
⎞⎠⎟ −
92+ 8
2= 0
24− 9
2+ 8
2= 0
12− 9
2+ 8
2= 0
0 = 0
2 −4( )2 + 9 −4( ) + 4 = 0
2 16( ) −36 + 4 = 0
32−36 + 4 = 0
0 = 0
X2 +13X − 68 = 0
X +17( ) X − 4( ) = 0
X +17 = 0
X = −17
X − 4 = 0
X = −4
−17( )2 + 13 −17( ) − 68 = 0
289 − 221− 68 = 0
0 = 0
4( )2 + 13 4( ) − 68 = 0
16 + 52 − 68 = 0
0 = 0
X2 − 2X + 5 = 8
X2 − 2X + 5 − 8 = 0
X2 − 2X − 3 = 0
X − 3( ) X + 1( ) = 0
X − 3 = 0
X = 3
X + 1= 0
X = −1
3( )2 − 2 3( ) + 5 = 8
9 − 6 + 5 = 8
8 = 8
−1( )2 − 2 −1( ) + 5 = 8
1+ 2 + 5 = 8
8 = 8
X2 − Y2 = X − Y( ) X + Y( )
X −4( )
X −4( )
8. XX
X
X X
X X
−× −
− ++ −
− +
44
4 16
4
8 16
2
2
9.
10.
X Y X Y X Y
X Y X Y
X Y
2 2
2 2 2 24 4 4
4
− = −( ) +( )
− = ( ) −( )= ( ) −( )) +( )
− = −( ) +( )= ( ) −( )( ) +
X Y
X Y X Y X Y
X Y X Y
or: 4 4 2 2 2 2
2 2
2 2
(( )= ( ) −( ) +( )4 X Y X Y
11.
12.
− − ( ) = − ×( ) − ( )( ) =− − = −
× =− −
3 2 3 3 2 2
9 4 13
4 4 4
2 2
2 3 2++
− × − ×
− + −( )
= =
( ) ( ) = =
= =
3 1
23
22
2 3 2 2
6 4 6 4
4 4
13. X X X X
X X X XX
B B B
B
B
B
B B B B B
2
2 11
4
4
1
2 1 1 4 4 1
2 3 5
2 3 5
2
14. − + =
− + =
−
− −
+ −
BB B B
B B B
B B or B B
3 1 4 4 1
3 3 5
3 5 5 3
3 5
2 3 5
5 5
− + =
− + =
− + −
− + +
15.
16.
B
B
B
R
R
4925
25 4 93625
1 1125
3 45 155 3 4 1
=
= ×
= =
=
= ×
.
. 555 51
515
10 15
10 2
520 65 8
24
R
R or
hours
=
= =
=
.
17.
18.
÷
00 6 40
4
2 2 2 4 28 2
2 8
÷ ==
+ = − => + ( ) = −+ = −
= − −
mph
19. X
Y X YY
YYY
Y X X
XX
= −
+ = − => −( ) + = −==
10
2 2 10 2 2
2 84
Alternately, yoou may take the value
for X directly from equatiion 2.
20. 3 4 2 3 2 4 2
3 62
X X X X X
X X
+( ) +( ) = ( ) +( ) + ( ) +( )= +(( ) + +( )4 8X
aLGeBra 1
sYsteMatic reVieW 27D - sYsteMatic reVieW 27e
soLutions272
B
B
B
R
R
4925
25 4 93625
1 1125
3 45 155 3 4 1
=
= ×
= =
=
= ×
.
. 555 51
515
10 15
10 2
520 65 8
24
R
R or
hours
=
= =
=
.
17.
18.
÷
00 6 40
4
2 2 2 4 28 2
2 8
÷ ==
+ = − => + ( ) = −+ = −
= − −
mph
19. X
Y X YY
YYY
Y X X
XX
= −
+ = − => −( ) + = −==
10
2 2 10 2 2
2 84
Alternately, yoou may take the value
for X directly from equatiion 2.
20. 3 4 2 3 2 4 2
3 62
X X X X X
X X
+( ) +( ) = ( ) +( ) + ( ) +( )= +(( ) + +( )4 8X
Systematic Review 27E SystematicReview 26E1. 4 8 3 0
2 1 2 3 0
2X X
X X
+ + =+( ) +( ) =
22 1 02 1
12
2 3 02 3
32
4 12
2
XX
X
XX
X
+ == −
= −
+ == −
= −
− +2. 88 1
23 0
4 14
82
3 0
1 4 3 00 0
4 32
− + =
− + =
− + ==
− + −
+ =
− + =
− + =
2
8 32
3 0
4 94
242
3 0
364
12 3 00
9 12 3 00 0
− + ==
3.
4.
X X
X X
XX
XX
2 7 12 0
3 4 0
3 03
4 04
3
+ + =+( ) +( ) =+ =
= −+ =
= −
−( )) + −( ) + =− + =
=
−( ) + −( ) + =−
2
2
7 3 12 0
9 21 12 00 0
4 7 4 12 016 28 ++ =
=12 00 0
3.
4.
X X
X X
XX
XX
7 12 0
3 4 0
3 03
4 04
3
+ + =+( ) +( ) =+ =
= −+ =
= −
−( )) + −( ) + =− + =
=
−( ) + −( ) + =−
2
2
7 3 12 0
9 21 12 00 0
4 7 4 12 016 28 ++ =
=12 00 0
5. X X
X X
X X
X X
X
2
2
2
1 13
1 13 0
12 0
4 3 0
4
+ + =+ + − =
+ − =+( ) −( ) =
+ = 004
3 03X
XX= −
− ==
6. −( ) + −( ) + =− + =
=
( ) + ( ) + =+
4 4 1 1316 4 1 13
13 13
3 3 1 13
9 3
2
2
++ ==
1 1313 13
7. X X X X−( ) −( ) = − +5 5 10 252
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
0
0 = 0
−4( )2 + 7 −4( ) + 12 = 0
16 − 28 + 12 = 0
0 = 0
X2 + X + 1= 13
X2 + X + 1− 13 = 0
X2 + X − 12 = 0
X + 4( ) X − 3( ) = 0
X + 4 = 0
X = −4
X − 3 = 0
X = 3
−4( )2 + −4( ) + 1= 13
16 − 4 + 1= 13
13 = 13
3( )2 + 3( ) + 1= 13
9 + 3 + 1= 13
13 = 13
16X2 − 4 = 4( ) 4X2 −1( ) =4( ) 2X −1( ) 2X +1( )
�or:
16X2 − 4 = 4X − 2( ) 4X + 2( ) =2( ) 2X −1( ) 2( ) 2X +1( ) = 4( ) 2X −1( ) 2X +1( )
X2 −100 = X −10( ) X +10( )
−3( )2 − 5( )2= 9 − 25 = −16
2−4 × 24 = 2−4+4 = 20 = 1
X2( )−3 X3( )−2 = X 2( ) −3( )X 3( ) −2( ) =
X−6X−6 = X−6+ −6( )X−12
5M4N2M−1− 2NM4
N−3M= 5M4+ −1( )N2 − 2N1M4N3M−1=
5M5N2 − 2N1+3M4+ −1( ) = 5M5N2 − 2M3N4
58= G
20
5 × 20 = 8G
100 = 8G
1008
X −5( )
X −5( )
8.
9.
X
X
X
X X
X X
X X
−× −
− +
−
− +
− = ( ) −(
5
5
5 25
5
10 25
16 4 4 4 1
2
2
2 2 )) = ( ) −( ) +( )
− = −( ) +( )= ( )
4 2 1 2 1
16 4 4 2 4 2
2 2
2
X X
X X X
X
or:
−−( )( ) +( )= ( ) −( ) +( )
− = −( )
1 2 2 1
4 2 1 2 1
100 102
X
X X
X X X10. ++( )
−( ) − ( ) = − = −
× = = =− − +
10
3 5 9 25 16
2 2 2 2
2 2
4 4 4 4 0
11.
12. 11
23
32
2 3 3 2
6 6 6
13. X X X X
X X X
( ) ( ) =
= =
− − ( ) −( ) ( ) −( )
− − − + −66 12
4 2 14
34 1 2 1 45 2 5 2
( ) −
−−
+ −( )
=
− = −
X
M N M NM
N MM N NM N14. 33 1
3 2 1 3 4 1
3 2 3 4
5 2
5 2
M
M N N M
M N M N
−
+ + −( )= −= −
aLGeBra 1
sYsteMatic reVieW 27e - Lesson Practice 28a
soLutions 273
− = −( )
1 2 2 1
4 2 1 2 1
100 10
X
X X
X X X10. ++( )
−( ) − ( ) = − = −
× = = =− − +
10
3 5 9 25 16
2 2 2 2
2 2
4 4 4 4 0
11.
12. 11
23
32
2 3 3 2
6 6 6
13. X X X X
X X X
( ) ( ) =
= =
− − ( ) −( ) ( ) −( )
− − − + −66 12
4 2 14
34 1 2 1 45 2 5 2
( ) −
−−
+ −( )
=
− = −
X
M N M NM
N MM N NM N14. 33 1
3 2 1 3 4 1
3 2 3 4
5 2
5 2
M
M N N M
M N M N
−
+ + −( )= −= −
15. 58 20
5 20 8100 8100
812 1
2
=
× ==
= =
G
GG
G
16.
17.
18
72
100
7 2 1007 200
2007
28 47
2 22
=
= ×=
= =
+ −
TTT
T
N N
.. N N
N N
N N
N N
N
2
2
2
2 2 22
2 2 22 0
2 24 0
6 4 0
+ − =+ − − =
+ − =+( ) −( ) =
++ == −
− ==
6 06
4 04N
NN
19. 5 6 3 15 3 184 3 20
19 38
Y X Y XY XY
Y
− = −( )( ) => − = −+ + = −
= −
= −33819
2
5 6 5 2 610 6
44
4
= −
− = − => −( ) − = −− − = −
− == −
− −
Y X XX
XX
, 22
2 3 1
3 1 2 3 1
3 2
( )+( ) +( ) =
( ) +( ) + ( ) +( ) =+( ) +
20. X X
X X X
X X 66 2X +( )
Lesson Practice 28ALessonPractice 27A1.
2.
1 12foot inches
F
=eet inn numerator to remain
final answer.
nches
in
I iin denominator
so they will cancel.
3. 84 1in × ft112
8412
7in
= =ft ft
4.
5.
3 1feet yard=Yards in numerator to remain inn final answer.
Feet in denominator so they willl cancel.
6. 63 1
3
633
21ftft
× = =yd yd yards
7.
8.
1 12foot inches
I
=nches in numerator to
remaain in final answer.
eet in denominator so
the
F
yy will cancel.
9. 15 121
1801
180
ftft
× = =in in in
10.
11.
4 1quarts gallon
Q
=uarts in numerator to reemain
in final answer.
Gallons in denominator
soo they will cancel.
12. 25 4 1001
100gal qt
gal
qt q× = = tt
13.
14.
16 1 oz lb
pounds in numerator
ounces in
=
ddenominator
g
15.
16.
272 116
17
4 1
oz lboz
lb
qt
× =
= aal
in numerator
in denominator
17. gallons
quarts
118. 52 1
413qt gal
qt× = gal
aLGeBra 1
Lesson Practice 28B - sYsteMatic reVieW 28c
soLutions274
Lesson Practice 28BLessonPractice 27B1.
2.
1 100meter centimeters=Ceentimeters in numerator to remain
in final answwer.
Meters in denominator
so they will cancel.
33.
4.
14 1001
1 4001
1 400
1
m cmm
cm cm
kilometer
× =
=, ,
== 1 000, meters
5. Meters in numerator to remain
inn final answer.
ilometers in denominator
so th
K
eey will cancel.
6. 200 1 0001
200 0001
2
km mkm
m
× =
=
,
, 000 000
1 10
, m
dekaliter liters7.
8.
=Dekaliters in numerator to remain
in final answer.
iters in L ddenominator
so they will cancel.
9. 3 500, liters × 1110
350010
350
1 1 0,
dklliters
dkl dkl
liter
=
=
=10. 000 milliliters
L11. iters in numerator to remain
in final answer.
illiliters in denominator
so
M
they will cancel.
12. 67 000 11 000
6
,,
ml literml
× =
77 0001 000
67
1 100
,,
liters liters
hectoliter
=
=13. liters
L14. iters in numerator to remain
in finaal answer.
ectoliters in denominator
so they w
H
iill cancel.
15. 4 5 1001
4501
. hl litershl
liters
× =
= 4450
1 10
liters
gram decigrams
G
16.
17.
=rams in nummerator to remain
in final answer.
s inDecigram denominator
so they will cancel.
18. 790 1
1dg g×
00
79010
79dg
g g= =
67 000 11 000
6
,,
ml literml
77 0001 000
67
1 100
,,
liters liters
hectoliter
=
=13. liters
L14. iters in numerator to remain
in finaal answer.
ectoliters in denominator
so they w
H
iill cancel.
15. 4 5 1001
4501
. hl litershl
liters
× =
= 4450
1 10
liters
gram decigrams
G
16.
17.
=rams in nummerator to remain
in final answer.
s inDecigram denominator
so they will cancel.
18. 790 1
1dg g×
00
79010
79dg
g g= =
Systematic Review 28CSystematicReview 27C1.
2.
12 1inches foot
F
=eet iin numerator to remain
in final answer.
nches I iin denominator
so they will cancel.
3. 60 1in × ft112
6012
5
3 1
in
feet yard
Yards
= =
=
ft ft
4.
5. in numeerator to remain
in final answer.
eet in denomF iinator
so they will cancel.
6. 24 1
3
24ftft
y× =yd dd yd3
8
16 1
=
=7.
8.
ounces pound
Pounds in numeratorr to remain
in final answer.
in denominaOunces ttor
so they will cancel.
9. 32 116
3216
oz lboz
lb× = ==
=
2
4 1
lb
quarts gallon
Gallons
10.
11. in numeratoor to
remain in final answer.
in denominQuarts aator
so they will cancel.
12. 28 1
4
28qts gal
qts× = gal gal
47=
SystematicReview 27C1.
2.
12 1inches foot
F
=eet iin numerator to remain
in final answer.
nches I iin denominator
so they will cancel.
3. 60 1in × ft112
6012
5
3 1
in
feet yard
Yards
= =
=
ft ft
4.
5. in numeerator to remain
in final answer.
eet in denomF iinator
so they will cancel.
6. 24 1
3
24ftft
y× =yd dd yd3
8
16 1
=
=7.
8.
ounces pound
Pounds in numeratorr to remain
in final answer.
in denominaOunces ttor
so they will cancel.
9. 32 116
3216
oz lboz
lb× = ==
=
2
4 1
lb
quarts gallon
Gallons
10.
11. in numeratoor to
remain in final answer.
in denominQuarts aator
so they will cancel.
12. 28 1
4
28qts gal
qts× = gal gal
47=
aLGeBra 1
sYsteMatic reVieW 28c - sYsteMatic reVieW 28D
soLutions 275
13. X R
X X X
−
− − +
−
3 4
2 5 102
XX X
X
X
2 2
3 10
3 6
−( )− +
− − + (( )
−4
214. X
× −− +
−
− +
X
X
X X
X X
3
3 6
2
5 6
2
2
++
− +
4
5 102X X
15. 3 10 3 0
3 1 3 0
3 1 03 1
13
3
2X X
X X
XX
X
X
+ + =+( ) +( ) =+ =
= −
= −
+ = 003
3 13
10 13
3 0
3 19
1
2
X = −
− + −
+ =
−
16.
003
93
0
39
103
93
0
13
103
93
0
0 0
3 3 10 32
+ =
− + =
− + =
=
−( ) + −( ) +33 0
3 9 30 3 0
27 30 3 00 0
10 2 6 1 32
=( ) − + =
− + ==
− + =17. ( )(. .X X ))
2 6 10 30
2 6 20 0
2 3 10 0
2 5 2
2
2
2
X X
X X
X X
X X
− + =− − =
− −( ) =−( ) +(( ) =
− ==
+ == −
( ) − ( ) + =( )
0
5 05
2 02
2 5 6 5 1 3
2 25
2
XX
XX
18. . .
. −− + =− + =
=
−( ) − −( ) + =( ) + + =
3 1 3
5 3 1 33 3
2 2 6 2 1 3
2 4 1 2 1
2. .
. . 338 1 2 1 3
3 3. .+ + =
=
( )(. .X X ))
2 6 10 30
2 6 20 0
2 3 10 0
2 5 2
2
2
2
X X
X X
X X
X X
− + =− − =
− −( ) =−( ) +(( ) =
− ==
+ == −
( ) − ( ) + =( )
0
5 05
2 02
2 5 6 5 1 3
2 25
2
XX
XX
18. . .
. −− + =− + =
=
−( ) − −( ) + =( ) + + =
3 1 3
5 3 1 33 3
2 2 6 2 1 3
2 4 1 2 1
2. .
. . 338 1 2 1 3
3 3. .+ + =
=
19. Q
Q
Q
Q or
..
.
22510
10 2 25
10 5
510
12
5
=
= ×=
= =
20. AB
CD
AD BC
A BCD
=
=
=
Systematic Review 28DSystematicReview 27D1.
2.
12 1inches foot
Inches
= in numerator to remain
in final answer.
iFeet nn denominator
so they will cancel.
3. 4 121
ft × infft
,
= =
=
481
48
1 5 280
in in
mile ft
Feet
4.
5. in numeraator to remain
in final answer.
in denomiMiles nnator
so they will cancel.
6. 3 5 2801
15
mimi
× =, ft
,, ft , ft
,
8401
15 840
2 000 1
=
=7.
8.
lb ton
Pounds in nnumerator to remain
in final answer.
in deTons nnominator
so they will cancel.
9. 6 2 000tons lb× ,11
12 0001
12 000
2 1
tonlb
lb
quart
= =
=
,
,
10.
11
pints
.. Pints in numerator to remain
in final answer.
QQ in denominator
so they will cancel.
uarts
2..5 2
1
51
5qt pt
qt
pt pt× = =
aLGeBra 1
sYsteMatic reVieW 28D - sYsteMatic reVieW 28e
soLutions276
3 5 2801
15
mimi
, ft
,, ft , ft
,
8401
15 840
2 000 1
=
=7.
8.
lb ton
Pounds in nnumerator to remain
in final answer.
in deTons nnominator
so they will cancel.
9. 6 2 000tons lb× ,11
12 0001
12 000
2 1
tonlb
lb
quart
= =
=
,
,
10.
11
pints
.. Pints in numerator to remain
in final answer.
QQ in denominator
so they will cancel.
uarts
12. 2..5 2
1
51
5qt pt
qt
pt pt× = =
13. 2 3 5 0
2 5 1 0
2 5 02 5
52
1 0
2X X
X X
XX
X
XX
− − =−( ) +( ) =− =
=
=
+ == −−1
14. 2 3 52
5 0
2 254
152
102
0
252
−
− =
− − =
5504
152
102
0
252
152
102
0
0 0
2 1 3 1 5 0
2
2
− − =
− − =
=
−( ) − −( ) − =11 3 5 02 3 5 0
0 0
( ) + − =+ − =
=
15. 3 8 4 0
3 2 2 0
3 2 03 2
23
2
2X X
X X
XX
X
X
+ + =+( ) +( ) =+ =
= −
= −
= −
16. 3 23
8 23
4 0
3 49
163
123
2
− + −
+ =
− + = 00
129
163
123
0
43
163
123
0
0 0
3 2 8 2 4 0
3
2
− + =
− + =
=
−( ) + −( ) + =44 16 4 016 16 4 0
0 0
( ) − + =− + =
=
17. 3 12 0
3 4 0
3 2 2 0
2 02
2
2
Y
Y
Y Y
YY
Y
− =( ) −( ) =
( ) −( ) +( ) =− ==
+22 02=
= −Y
18. 3 2 12 0
3 4 12 012 12 0
0 0
3 2 12 0
3 4
2
2
( ) − =( ) − =
− ==
−( ) − =( ) −− =
− ==
= × = =
12 012 12 0
0 0
651
31
1951
19519. X mi mi mihr
hr
220. X mi mi mi= × = =451
51
2251
225hr
hr
Systematic Review 28ESystematicReview 27E1.
2.
12 1 inches foot
Inches
= in numerator to remain
in final answer.
iFeet nn denominator
so they will cancel.
3. 7 920 12, ft ×ft
, ,
,
in
in in
pounds to
1
95 0401
95 040
2 000 1
=
=
=4. nn
Tons5. in numerator to remain
in final answer..
in denominator
so they will cancel.
Pounds
aLGeBra 1
sYsteMatic reVieW 28e - Lesson Practice 29a
soLutions 277
in numerator to remain
in final answer.
iFeet nn denominator
so they will cancel.
3. 7 920 12, ft ×ft
, ,
,
in
in in
pounds to
1
95 0401
95 040
2 000 1
=
=
=4. nn
Tons5. in numerator to remain
in final answer..
in denominator
so they will cancel.
Pounds
6. 10 000 12 000
10 0002 000
5
,,
,,
lb tonlb
tons ton
×
= = ss
ounces pound
Ounces
7.
8.
16 1= in numerator to reemain in final
answer. in denominator sPounds oo
they will cancel.
9. 5 161
801
80lb ozlb
oz oz× = =
110.
11.
2 1pints
ints in numerator to rem
= quart
P aain in final
answer. in denominator so Quarts tthey
will cancel.
12. 13 2
1
261
26qt pt
qt
pt pt× = =
13. 2 6 0
2 3 2 0
2 3 02 3
32
2 0
2X X
X X
XX
X
XX
+ − =−( ) +( ) =− =
=
=
+ == −22
14. 2 32
32
6 0
2 94
32
122
0
184
2
+
− =
+ − =
++ − =
+ − =
=
−( ) + −( ) − =( ) − −
32
122
0
92
32
122
0
0 0
2 2 2 6 0
2 4 2 6
2
==− − =
=
08 2 6 0
0 0
15. 5 125 0
5 25 0
5 5 5 0
5 05
2
2
B
B
B B
BB
− =( ) −( ) =
( ) −( ) +( ) =− =
=BB
B+ =
= −5 0
5
16. 5 5 125 0
5 25 125 0
125 125 00 0
5 5 125
2
2
( ) − =( ) − =
− ==
−( ) − ==( ) − =
− ==
0
5 25 125 0
125 125 00 0
17. 6 6 18 90
6 6 72 0
6 12 0
6 4
2
2
2
X X
X X
X X
X
− + =− − =
( ) − −( ) =( ) −( )) +( ) =− =
=+ =
= −
( ) − ( ) + =
X
XX
XX
3 0
4 04
3 03
6 4 6 4 18 90
6 1
218.
66 24 18 90
96 24 18 9090 90
165
( ) − + =− + =
=
=19. X mi mihr ..
.mph
. hr
hr5 6
6 5 1212
108
XX mi
rate
R mi
== ==
=
÷
20. == 12 5. mph
Lesson Practice 29ALessonPractice 28A
1. 11
121
121
142ft
ft ft× × =in in 44
21
121
121
288
1
1
2
22
2
ft
ft ft
in
in in in
yd
2.
3.
× × =
× 331
31
9
1
1361
361
2
3
ft ft ftyd yd
yd inyd
inyd
× =
× ×4. ×× =
× × ×
361
46 656
21
121
121
3
3
,
ft
ft ft
inyd
in
in in5. 1121
3 456 3
ft,in in=
aLGeBra 1
Lesson Practice 29a - sYsteMatic reVieW 29c
soLutions278
1. 11
121
121
14ft
ft ft× × =in in 44
21
121
121
288
1
1
2
22
2
ft
ft ft
in
in in in
yd
2.
3.
× × =
× 331
31
9
1
1361
361
2
3
ft ft ftyd yd
yd inyd
inyd
× =
× ×4. ×× =
× × ×
361
46 656
21
121
121
3
3
,
ft
ft ft
inyd
in
in in5. 1121
3 456 3
ft,in in=
6.
7.
81
101
101
800
9
1361
2
2
2
cm mmcm
mmcm
mm
yd in
× × =
×yyd
inyd
in
mi
mi
× =
× ×
361
11 664
11
5 2801
5 28
2
2
,
, ft ,8. 001
27 878 400
1001
1
3
1
3
2
2
ft
, , ft
ft
ft
mi
yd yd
=
× ×9.ft
.
. ft ft .
≈11 11
5
131
31
4 5
2
22
yd
yd
yd ydyd10. × × =
111. 3001
15 280
15 280
00001
2ft
, ft , ft
.
× ×mi mi
mi
≈
22
22950
11
1001
100095
43
12.
13.
.
,
cm mcm
mcm
m× × =
5560
4 4 8 128
3
2
3
ft
ft ft ft ft
ft
14.
15.
× × =
× ft ft ft
ft ft ft
3 3 27
3 3 9
3
2
× =
=16. x
Lesson Practice 29B
1.
2.
71
121
121
1 008
31
100
22
2
ft
ft ft,× × =
×
in in in
m cmmm
cmm
cm
in
1100
130 000
81
121
12
2
2
,
. ft
ft
× =
× ×3. iin in
in in
1115 2
1 51
121
121
216
2
2
ft.
. ft
ft ft
=
× × =4.
,
in
m dmm
dmm
dmm
dm
2
3
3
81
101
101
101
8 000
5.
6.
× × × =
331
1 0001
1 0001
1 0001
3 000 0
3km mkm
mkm
mkm
× × × =, , ,
, , 000 000
5 61
121
121
121
3
3
,
. ft
ft ft ft
m
in in in7. × × × =
99 676 8
21
121
121
121
3
3
, .
ft
ft ft ft
in
in in in
1.
2.
71
121
121
1 008
31
100
22
2
× × =
×
in in in
m cmmm
cmm
cm
in
1100
130 000
81
121
12
2
2
,
. ft
ft
× =
× ×3. iin in
in in
1115 2
1 51
121
121
216
2
2
ft.
. ft
ft ft
=
× × =4.
,
in
m dmm
dmm
dmm
dm
2
3
3
81
101
101
101
8 000
5.
6.
× × × =
331
1 0001
1 0001
1 0001
3 000 0
3km mkm
mkm
mkm
× × × =, , ,
, , 000 000
5 61
121
121
121
3
3
,
. ft
ft ft ft
m
in in in7. × × × =
99 676 8
21
121
121
121
3
3
, .
ft
ft ft ft
in
in in in8. × × × = 33 456
7
1361
361
361
3
3
, in
yd inyd
inyd
inyd
9. × × × ==
326 592 3, in
10. 41
5 2801
5 2801
5 2801
12
3mi
mi mi mi× × × ×, ft , ft , ft
ft ft ft
, , , , ,
in in in1
121
121
1 017 400 000 000 000
× × ≈
in
cm mcm
mcm
mcm
3
33701
1100
1100
1100
11. × × × =
..
.
00037
181
1100
1100
0018
3
2
m
cm mcm
mcm
m12. × × = 22
222
143 560
187 120
4
13.
14.
, ft , ft
f
acresacre
× =
tt ft ft ft
ft
× × =
×
4 8 128
2
1271
3
315.
yards
yarrd
yards
yard
=
× =
54
2
19
118
3
22
ft
ft ft16.
Systematic Review 29CSystematicReview 29C
1. 11
121
121
2ftft ft
× ×in in ==
× × =
144
1
131
31
9
11
2
22
2
ft ft ft
in
yd
yd yd
mi
2.
3. ×× ×
=
5 2801
5 2801
27 878 400
11
2
2
, ft , ft
, , ft
mi mi
m4. ×× × =
×
1001
1001
10 000
41
121
2
2
,
ftft
cmm
cmm
cm
in5. ×× =121
576 2
ftin in
aLGeBra 1
sYsteMatic reVieW 29c - sYsteMatic reVieW 29c
soLutions 279
SystematicReview 29C
1. 11
121
121
2ftft ft
× ×in in ==
× × =
144
1
131
31
9
11
2
22
2
ft ft ft
in
yd
yd yd
mi
2.
3. ×× ×
=
5 2801
5 2801
27 878 400
11
2
2
, ft , ft
, , ft
mi mi
m4. ×× × =
×
1001
1001
10 000
41
121
2
2
,
ftft
cmm
cmm
cm
in5. ×× =121
576 2
ftin in
6.
7.
7
131
31
63
3 21
5 280
22
2
ft ft ft
. ,
yd
yd yd
mi
× × =
× ft , ft
, , ft
.
15 280
1
89 210 880
15 71
10
2
2
mi mi
m
× =
×8. 001
1001
157 000
43 560
3
2
2
,
, ft
ft
cmm
cmm
cm
× =
9.
10. ft ft× =
− + =−( ) −( ) =− =
3 9
3 5 2 0
3 2 1 0
3 2
2
211. X X
X X
X 003 2
23
1 01X
X
XX=
=
− ==
12. 3 23
5 23
2 0
3 49
103
63
0
12
2
−
+ =
− + =
99103
63
0
43
103
63
0
0 0
3 1 5 1 2 0
3 1 5 2
2
− + =
− + =
=
( ) − ( ) + =( ) − + ==
− + ==
− + =( ) − +( ) =( ) −
03 5 2 0
0 0
2 10 12 0
2 5 6 0
2
2
2
13. X X
X X
X 33 2 0
0 0
3 03
2 02
2 3 10 3 122
( ) −( ) ==
− ==
− ==
( ) − ( ) +
X
XX
XX
14. ==( ) − + =
− + ==
( ) − ( ) + =(
0
2 9 30 12 0
18 30 12 00 0
2 2 10 2 12 0
2 4
2
))
99103
63
0
43
103
63
0
0 0
3 1 5 1 2 0
3 1 5 2
2
− + =
− + =
=
( ) − ( ) + =( ) − + ==
− + ==
− + =( ) − +( ) =( ) −
03 5 2 0
0 0
2 10 12 0
2 5 6 0
2
2
2
13. X X
X X
X 33 2 0
0 0
3 03
2 02
2 3 10 3 122
( ) −( ) ==
− ==
− ==
( ) − ( ) +
X
XX
XX
14. ==( ) − + =
− + ==
( ) − ( ) + =(
0
2 9 30 12 0
18 30 12 00 0
2 2 10 2 12 0
2 4
2
)) − + =− + =
=
−( ) = −( ) −( ) = −
20 12 08 20 12 0
0 0
4 4 4 82 215. X X X X XX +
> ×>
16
35 32 381 225 1 216
216., ,
17. X X X X2 7 10 2 5+ + = +( ) +( )
13.
14.
15.
16.
17.
18.
19.
20.
0
2X2 −10X +12 = 0
2( ) X2 −5X + 6( ) = 0
2( ) X −3( ) X − 2( ) = 0
X −3 = 0
X = 3
X − 2 = 0
X = 2
2 3( )2 −10 3( ) +12 = 0
2 9( ) −30 +12 = 0
18 −30 +12 = 0
0 = 0
2 2( )2 −10 2( ) +12 = 0
2 4( ) − 20 +12 = 0
8 − 20 +12 = 0
0 = 0
X − 4( )2 = X − 4( ) X − 4( ) =X2 − 8X +16
352 32×38
1,225 >1,216
WF × 9�ft2 = 1�ft2
WF = 1�ft2
9�ft2= 1
9
X +2( )
X +5( )
3X +2( )
X +2( )
18. 3 2 2 3 8 42X X X X+( ) +( ) = + +
13.
14.
15.
16.
17.
18.
19.
20.
0
2X2 −10X +12 = 0
2( ) X2 −5X + 6( ) = 0
2( ) X −3( ) X − 2( ) = 0
X −3 = 0
X = 3
X − 2 = 0
X = 2
2 3( )2 −10 3( ) +12 = 0
2 9( ) −30 +12 = 0
18 −30 +12 = 0
0 = 0
2 2( )2 −10 2( ) +12 = 0
2 4( ) − 20 +12 = 0
8 − 20 +12 = 0
0 = 0
X − 4( )2 = X − 4( ) X − 4( ) =X2 − 8X +16
352 32×38
1,225 >1,216
WF × 9�ft2 = 1�ft2
WF = 1�ft2
9�ft2= 1
9
X +2( )
X +5( )
3X +2( )
X +2( )
19.
20.
WF
WF
WF
× =
= = =
× =
3 1
13
333 33 13
9 12
ft ft
. %
ft fft
ft
ft
2
2
21
9
19
WF = =
aLGeBra 1
sYsteMatic reVieW 29D - sYsteMatic reVieW 29e
soLutions280
Systematic Review 29DSystematicReview 28D
1. 91
121
121
2ftft
× ×in infft
,
ft ft ft
=
× × =
1 296
5
13
13
145
2
22
in
yd
yd yd2.
3.. 61
5 2801
5 2801
167 270 400
2 , ft , ft
, ,
mimi mi
× × =
fft
,
.
2
2218
1100
1100
1180 0004.
5.
m cmm
cmm
cm× × =
7751
121
121
108
1 3
1
22
2
ftft ft
.
× × =
×
in in in
yd6. 33
13
111 7
251
5 2801
2
2
ft ft . ft
, ft
yd yd
mi
× =
×7.mmi mi
m c
× =
×
5 2801
696 960 000
671
100
2
2
, ft
, , ft
.8. mmm
cmm
cm
acres
1100
16 700
51
43 5601
2
2
,
, ft
× =
×9. , ft
ft
acre
cordscord
=
× =
217 800
21
1281
256
2
310. ft3
11.
12.
3 9 12 0
3 3 4 0
3 31
4 04
2X X
X X
XX
XX
− − =+( ) −( ) == −= −
− ==
33 1 9 1 12 0
3 1 9 12 03 9 12 0
0 0
3 4 9
2
2
−( ) − −( ) − =( ) + − =
+ − ==
( ) − 44 12 0
3 16 36 12 0
48 36 12 00 0
( ) − =( ) − − =
− − ==
13.
14.
X
X X
XX
XX
2
2
36 0
6 6 0
6 06
6 06
6
− =−( ) +( ) =− =
=+ =
= −
( ) −336 0
36 36 00 0
6 36 0
36 36 00 0
5
2
2
=− =
=
−( ) − =− =
=
−( ) = −15. X X 55 5 10 25
45 40 502 025 2 000
2
2
2
( ) −( ) = − +
> ×>
X X X
X
13.
14.
X
X X
XX
XX
2
2
36 0
6 6 0
6 06
6 06
6
− =−( ) +( ) =− =
=+ =
= −
( ) −336 0
36 36 00 0
6 36 0
36 36 00 0
5
2
2
=− =
=
−( ) − =− =
=
−( ) = −15. X X 55 5 10 25
45 40 502 025 2 000
2
2
2
( ) −( ) = − +
> ×>
X X X
X
16.
17.
, ,
++ + = +( ) +( )10 21 7 3X X X
0
X − 6 = 0
X = 6
X + 6 = 0
X = −6
6( )2 − 36 = 0
36 − 36 = 0
0 = 0
−6( )2 − 36 = 0
36 − 36 = 0
0 = 0
X − 5( )2 = X − 5( ) X − 5( ) = X2 − 10X + 25
452 40 × 50
2,025 > 2,000
WF × 144�in2 = 1�in2
WF = 1144
X + 3( )
X + 7( )
X + 3( )
X − 9( )
18. X X X X+( ) −( ) = − −3 9 6 272
0
X − 6( ) X + 6( ) = 0
X − 6 = 0
X = 6
X + 6 = 0
X = −6
6( )2 − 36 = 0
36 − 36 = 0
0 = 0
−6( )2 − 36 = 0
36 − 36 = 0
0 = 0
X − 5( )2 = X − 5( ) X − 5( ) = X2 − 10X + 25
452 40 × 50
2,025 > 2,000
WF × 144�in2 = 1�in2
WF = 1144
X + 3( )
X + 7( )
X + 3( )
X − 9( )19.
20.
WF in in
WF
WF i
× =
= =
×
36 1
136
0 2 7 2 8
144
. . % ≈
nn in
WF
2 21
1144
=
=
Systematic Review 29ESystematicReview 28E
1. 271
1
3
1
3
2ft
ft ft× ×yd yd ==
× × =
3
3
13
13
127
10 000
2
22ft ft ft
,
yd
yd
yd yd2.
3. fft
, ft , ft
.
,
2
2
11
5 2801
5 280
00036
1 2
× ×mi mi
mi
≈
4. 0001
1100
1100
12
11
12
22
3
cm mcm
mcm
m
in
× × =
×
.
ft5.11
121
121
1 728
1
13
3
3
ft ft ft,
ft
× × =
×
in in in
yd6.
113
13
127
11
5 2801
3
3
ft ft ft
, ft
yd yd yd
mi
× × =
×
7.
, ft , ft
, , ,
mi mi mi× ×5 280
15 280
1
147 000 000 000
≈
fft
, ,
aLGeBra 1
sYsteMatic reVieW 29e - Lesson Practice 30a
soLutions 281
3
3
13
13
127
10 000
ft ft ft
,
yd
yd
yd yd2.
3. fft
, ft , ft
.
,
2
2
11
5 2801
5 280
00036
1 2
× ×mi mi
mi
≈
4. 0001
1100
1100
12
11
12
22
3
cm mcm
mcm
m
in
× × =
×
.
ft5.11
121
121
1 728
1
13
3
3
ft ft ft,
ft
× × =
×
in in in
yd6.
113
13
127
11
5 2801
3
3
ft ft ft
, ft
yd yd yd
mi
× × =
×
7.
, ft , ft
, , ,
mi mi mi× ×5 280
15 280
1
147 000 000 000
≈
fft
, ,
3
331
1001
1001
1001
3 000
8. m cmm
cmm
cmm
× × ×
= 0000
31
1281
384
2
3
33ft ft
cm
cords
cord
yard
9.
10.
× =
ss
yard
X X
X X
1271
54
10 25 0
5 5
33
2
× =
− + =−( ) −( )
ft ft
11.
==− =
=
( ) − ( ) + =− + =
=
0
5 05
5 10 5 25 0
25 50 25 05
2
XX
X
12.
13.
14.
X X
X X
XX
XX
2 12 35 0
7 5 0
7 07
5 05
7
− + =−( ) −( ) =− =
=− =
=
( )) − ( ) + =− + =
=
( ) − ( ) + =−
2
2
12 7 35 049 84 35 0
0 0
5 12 5 35 0
25 60 ++ ==
35 00 0
15.
16.
3 1 2 3 7 2
73 77 60 80
5 621 4 80
2X X X X−( ) −( ) = − +× > ×
>, , 00
9 1
19
1 1 11 1
27 8
2 217.
18.
WF
WF
WF
× =
= = =
×
ft ft
. . %
, 778 400 43 560
43 56027 878 400
164
2 2, ft , ft
,, ,
=
=
=
WF
WF00
1009
11 1 1
2005
19.
20.
R
R mi
= =
=
ydsec
. yd/sec
hrr= 40 mph
15.
16.
3 1 2 3 7 2
73 77 60 80
5 621 4 80
2X X X X−( ) −( ) = − +× > ×
>, , 00
9 1
19
1 1 11 1
27 8
2 217.
18.
WF
WF
WF
× =
= = =
×
ft ft
. . %
, 778 400 43 560
43 56027 878 400
164
2 2, ft , ft
,, ,
=
=
=
WF
WF00
1009
11 1 1
2005
19.
20.
R
R mi
= =
=
ydsec
. yd/sec
hrr= 40 mph
Lesson Practice 30A1.
2.
3.
4.
5.
6.
2 5
9
1 6
28
101
621
6 2
45
.
.
.
. .km mikm
mi
o
× =
zz g
ozg
kg lbkg
lb
128
11 260
21
12 21
46 2
1
× =
× =
,
. .7.
8.55
19
113 5
151
41
6
25
1
yd . .
.
× =
× =
myd
m
cm incm
in
g
9.
10. ×× =. .0351
875ozg
oz
11.
12.
5
195
14 75
541
2 5
qt litersqt
liters
in c
× =
×
. .
. mmin
cm
km mikm
mi
lb
1135
51
621
3 1
451
4
=
× =
×
. .
.
13.
14. 55
120 25
1051
28
12 940
63
.
,
kg
lbg
oz g
ozg
=
× =
k
15.
16.yyd . .
191
56 7× =myd
m
aLGeBra 1
Lesson Practice 30B - sYsteMatic reVieW 30c
soLutions282
Lesson Practice 30BLessonPractice 29B1.
2.
3.
4.
5.
.
.
.
.
4
1 1
2 2
1 06
251cm × ..
. .
41
10
36
1035
11 26
12
1
incm
in
g ozg
oz
qt
=
× =
×
6.
7. .. .
.
951
11 4
1101
2 51
27
litersqt
liters
in cmin
=
× =8. 55
361
2 51
90
75 5
1035
1
.
. .
cm
in cmin
cm
g ozg
9.
10.
× =
× ==
× =
×
2 64
18 5
191
16 65
55
12 2
.
. yd . .
.
oz
myd
m
kg
11.
12.
. . .
lbskg
lb
mi kmmi
km
1121
16 31
1 61
26 08
=
× =13.
14. 3361
1 06
138 16
5 051
28
liters qt
literqt
oz
× =
×
. .
.15. gg
ozg
cm incm
in
1141 4
360 51
41
144 2
=
× =
.
. . .16.
Systematic Review 30CSystematicReview 29C1.
2.
51
2 51
12 5in cmin
cm× =. .
33
195
12 85
101
28
1
qt litersqt
liters
oz g
oz
× =
× =
. .
3. 2280
621
45
127 9. .
g
lb kg
lbkg4. × =
5. 3 4
2 1 6 5 9 1
6 3
2
3 2
3 2
X X
X X X X
X X
+ +
+ + + +
− +( )
2 9
2
8 1
8 4
3
2
2
X X
X X
X
X
R
+
− +( )+
− +( )−
−33
6. 3 2 4
2 1
3 2 4
6 3 2 2 8
6 3 5 2 9 4
3
6
X X
X
X X
X X X
X X X
+ +× +
+ +
+ +
+ + +−
XX X X3 5 2 9 1+ + +
7.
8.
9 3
9 10 3 10
9 10 000 3 100
90 000
4 2
4 2
X X=
( ) = ( )( ) = ( )
=
,
, 3300
300 300
3 51
43 5601
152 460
2
=
× =9. . , ft
,
acres
acre
fft
, ft , ft
, ,
2
211
5 2801
5 2801
27 878 4
10. mi
mi mi× × =
000
13 17 16 14221 224
5 50
5
2
2 2
ft
ft
11.
12.
× < ×<
=yd
yd222
2 2
2
13
13
145
5 45
45
× × =
=
<
ft ft ft
ft
ft
yd yd
yd
550
6 6 6
12 36
2
2
2
ft
13. X X X
X X
+( ) = +( ) +( ) =+ +
aLGeBra 1
sYsteMatic reVieW 30c - sYsteMatic reVieW 30D
soLutions 283
14. X Y
Y X
Y X
m
− =− = − +
= −
=
2 4
2 4
12
2
12
15. X X
X X
X X
2
2
5 6 20
5 14 0
7 2 0
+ + =
+ − =+( ) −( ) =
X
X
+ == −
7 0
7X
X
− ==
2 0
2
16. −( ) + −( ) + =− + =
=
( ) + ( )
7 5 7 6 2049 35 6 20
20 20
2 5 2
2
2 ++ =
+ + ==
6 204 10 6 20
20 20
17. 2 3 2 2 2 3 2
2 4 3 62
X X X X X
X X X
+( ) +( ) = ( ) +( )+( ) +( ) =+ + +( )
118.
19.
E W
earnings W weeks
= −= =( )400 100
E
see graph
,
$$
,
300
400 100
400 30 100
12 000 100
11
20. E W
E
E
E
= −= ( ) −= −= ,,900
Y
X
#18
X2 +12X + 6
X − 2Y = 4
−2Y = −X + 4
Y = 12
X − 2
m = 2
X2 +5X + 6 = 20
X2 +5X −14 = 0
X +7( ) X − 2( ) = 0
X +7 = 0
X = −7
X − 2 = 0
X = −2
−7( )2 +5 −7( ) + 6 = 20
49 −35+ 6 = 20
20 = 20
2( )2 +5 2( ) + 6 = 20
4 +10 + 6 = 20
20 = 20
2X +3( ) X + 2( ) = 2X( ) X + 2( ) + 3( ) X + 2( ) =
2X2 + 4X +3X + 6( )
E = 400W −100
E = 400 30( ) −100
E = 12,000 −100
E = 11,900
17. 2 3 2 2 2 3 2
2 4 3 62
X X X X X
X X X
+( ) +( ) = ( ) +( )+( ) +( ) =+ + +( )
118.
19.
E W
earnings W weeks
= −= =( )400 100
E
see graph
,
$$
,
300
400 100
400 30 100
12 000 100
11
20. E W
E
E
E
= −= ( ) −= −= ,,900
Systematic Review 30DSystematicReview 29D1.
2.
71
1 61
11 2mi kmmi
km× =. .
881
45
13 6
4
191
3 6
2
lb kg
lbkg
myd
m
qt
× =
× =
. .
yd . .3.
4.11
951
1 9× =. .litersqt
liters
5. 2 5 14 21
2 2 9 4 7
2 4
5
2
3 2
3 2
2
X X R
X X X X
X X
X
− − −
− − − +
− −( )− −−
− − +( )− +
− − +( )−
4
5 10
14 7
14 28
21
2
X
X X
X
X
6. 2 5 14
2
4 10 28
2 5 14
2 9 4
2
2
3 2
3 2
X X
X
X X
X X X
X X X
− −× −
− + +
− −
− − ++−
− − +
=
=
2821
2 9 4 7
16 4
100 000
3 2
2
2 4 2
X X X
X X
Y X YX
7.
8.
9. , fft
, ft
.
.
2
2
2
11
43 560
2 296
1 341
100
×
×
acre
acres
m
≈
10.
,
cmm
cmm
cm
1100
1
13 400 2
×
=
11.
12.
82 88 86 847 216 7 224
7 3 175 3
7 3
1
× < ×<
>
×
, ,
ftyd
yd 331
31
31
189 3
189 3 175 3
ft ft ft ft
ft ft
yd yd yd× × =
>
113. X X X X X−( ) = −( ) −( ) = − +32
3 3 2 6 9
aLGeBra 1
sYsteMatic reVieW 30D - sYsteMatic reVieW 30e
soLutions284
11.
12.
82 88 86 847 216 7 224
7 3 175 3
7 3
1
× < ×<
>
×
, ,
ftyd
yd 331
31
31
189 3
189 3 175 3
ft ft ft ft
ft ft
yd yd yd× × =
>
113. X X X X X−( ) = −( ) −( ) = − +32
3 3 2 6 9
14. X YY X
Y X
m
− =− = − +
= −
= −
2 42 4
12
2
2 negative reciprocall of 12
15. X X
X X
X X
2 12 35 152 12 20 0
10 2 0
− + =
− + =−( ) −( ) =
X
X
− ==
10 0
10
X
X
− ==
2 0
2
16. 102
12 10 35 15
100 120 35 15
15 15
( ) − ( ) + =− + =
=
22
12 2 35 15
4 24 35 15
( ) − ( ) + =− + =
17. 2 7 2
2 2 7 2
2 2 4 7 14
X X
X X X
X X X
+( ) +( ) =( ) +( ) + ( ) +( ) =
+ + +( ))=
=
=
=
18.
19.
D RT
T
T DR
T
divide both sides by R:
DR
1226
2( )( ) = hours
20. 2 3 2
32
1
Y X
Y X
< −
< −
try
false
, :
;
0 0
0 32
0 1
0 0 10 1
( )( ) < ( ) −
< −< −
try
true
, :
;
2 2
2 32
2 1
2 3 12 2
−( )−( ) < ( ) −− < −− <
see graphh
17.
18.
19.
20.
15
2X +7( ) X + 2( ) = 2X( ) X + 2( ) + 7( ) X + 2( ) =2X2 + 4X +7X +14( )D = RT�divide both sides by T:
DR= T
T = DR
T = 12( )6( )
= 2�hours
Y
X
Systematic Review 30E SystematicReview 29E1.
2
251
621
15 5km mikm
mi× =. .
..
3.
4
71
1 1
17 7
11
12 21
24 2
m
m
kg lbkg
lb
× =
× =
. yd . yd
. .
.. 101
1 06
110 6liters qt
literqt× =. .
5. 2 2 3 8 21
2 3 4 3 0 2 7 3
4 3 6 2
6 2
X X R
X X X X
X X
X
+ +
− + + −
− −( )+77
6 2 9
16 3
16 24
21
2 2 3 82 3
6 2
X
X X
X
X
X XX
X
− −( )−
− −( )
+ +× −
−
6.
−− −
+ +
+ −+
+ −
9 24
4 3 6 2 16
4 3 7 24
21
4 3 7 3
X
X X X
X X
X X
aLGeBra 1
sYsteMatic reVieW 30e - Lesson Practice 31a
soLutions 285
2 2 3 8 21
2 3 4 3 0 2 7 3
4 3 6 2
6 2
X X R
X X X X
X X
X
+ +
− + + −
− −( )+77
6 2 9
16 3
16 24
21
2 2 3 82 3
6 2
X
X X
X
X
X XX
X
− −( )−
− −( )
+ +× −
−
6.
−− −
+ +
+ −+
+ −
9 24
4 3 6 2 16
4 3 7 24
21
4 3 7 3
X
X X X
X X
X X
7.
8.
9.
1
144 12
25 6 5 3
1 75
19 2
115 75 2
=
=
× =
X X
yd
. yd ft . ft
00. 25 18 450 2
450 2
11
9 250
× =
× =
ft
ft
ft
yd yards of caarpet
yd
yd
11.
12.
13 17 16 14
221 224
5 2 50 2
5 2
1
× < ×<
< ft
×× × =
<
−( ) = −
3 3 45 2
45 2 50 2
22
ft ft ft
ft ft
yd yd
X X13. 22 2
2 4 4
42
4 4
2 8 16
( ) −( ) =− +
+( ) = +( ) +( ) =+ +
X
X X
X X X
X X
14.
7.
8.
9.
1
144 12
25 6 5 3
1 75
19 2
115 75 2
=
=
× =
X X
yd
. yd ft . ft
00. 25 18 450 2
450 2
11
9 250
× =
× =
ft
ft
ft
yd yards of caarpet
yd
yd
11.
12.
13 17 16 14
221 224
5 2 50 2
5 2
1
× < ×<
< ft
×× × =
<
−( ) = −
3 3 45 2
45 2 50 2
22
ft ft ft
ft ft
yd yd
X X13. 22 2
2 4 4
42
4 4
2 8 16
( ) −( ) =− +
+( ) = +( ) +( ) =+ +
X
X X
X X X
X X
14.
15. X X
X X
X X
2 7 18 422 7 60 0
12 5 0
+ − =
+ − =+( ) −( ) =
X
X
+ == −
12 0
12
X
X
− ==
5 0
5
16. −( ) + −( ) − =− − =
=
122
7 12 18 42
144 84 18 42
42 42
52
7 5 18 42
25 35 18 42
42 42
( ) + ( ) − =+ − =
=
17. T hour
X
= ÷ = =
=
4 6 46
23
60
To change to minutes:
23
(( ?)How many 60ths of an hour is 23
2 60 3
12
( ) ( ) = X
00 3
1203
40
=
= =
X
X minutes
18. T
X
X
X
= ÷ = =
=
( ) ( ) ==
4 3 43
1 13
604 60 3
240 3
hours
43
22403
80
1 20
= =X
or hour and
minutes
minutes
19.
20.
2 2 7
2 2 7
2 5
2 5 11
2 1
P P P
P P P
P
P
P
− + + − =+ − − + =++ =
= 11 5
2 6
62
3
−=
= =
P
P
Lesson Practice 31ALessonPractice 30A
1.
2.
16 16 4 64
2 2 4
32
33
21 2
= ( ) = =
= =
33.
4.
5.
100 100 10
8 8 2 4
12
23 3 2
2
51
110 5
1
= =
= = =
( ) =
X X
= = =
( ) =
110
510
12
13
15 1
315
X X X
Y Y6.
+
(
=
⋅( ) = ( ) = ( ) =
Y or Y
Y Y Y Y
Y
115 15
3 514 3 5
14 8
14
8
7.
))
=
= = =
( )
14 2
34 4 3
3
13
41
4
16 16 2 8
27 3 81
Y
8.
9.
10..
11.
aLGeBra 1
Lesson Practice 31a - sYsteMatic reVieW 31c
soLutions286
1.
2.
16 16 4 64
2 2 4
= =
= =
33.
4.
5.
100 100 10
8 8 2 4
12
23 3 2
2
51
110 5
1
= =
= = =
( ) =
X X
= = =
( ) =
110
510
12
13
15 1
315
X X X
Y Y6.
+
(
=
⋅( ) = ( ) = ( ) =
Y or Y
Y Y Y Y
Y
115 15
3 514 3 5
14 8
14
8
7.
))
=
= = =
( ) = =
14 2
34 4 3
3
13
41
4
16 16 2 8
27 3 81
Y
8.
9.
10..
11.
8 16 8 16 2 16 32
64 64
13 3
12
23 1
223
⋅ = ⋅ = ⋅ =
( ) =
+
= = =
⋅( ) = ( ) = ( ) =
64 64 413 3
5 712 5 7
12 12
1212. X X X X
XX X
M M M M
12 12 6
12
23
61 1
223
61 3
6
( )
+ +
=
⋅( ) = ( ) =13.446
61
76
61 7
661 7
35
5
( ) =
( ) = =
( ) ⋅
M M M
X X14.
= ⋅ =
=
( )( )
+
12
3 5 512
15 512 15 5
X X
X X X = =
=
( )
( )
12 20
12
20 12 10
523
X
X X
X15.
116 5 2
316
1018
59 9
5
= = =
( )
( )
X X
X or X
M16. 8812
34 8 1
234
248 3( )
= = =
( )
M M M
Lesson Practice 31BLessonPractice 30B
1.
2.
32 32 2 4
9 9 7
25 5
22
31 3
= ( ) = =
= = 229
81 81 9
625 625 5 125
12
34 4
33
613
6
3.
4.
5.
= =
= ( ) = =
( ) =X X(( )
= =
( ) = =
13
63 2
12
17 1
217
X X
Y Y Y6.11
14 14
4 615 4 6
15 10
15
10 1
or Y
Y Y Y Y
Y
7. ⋅( ) = ( ) = ( ) =+
( )(55 105 2
23 3
22
14
51 1
4
) = =
=
Y Y
1.
2.
32 32 2 4
9 9 7
25 5
22
31 3
= ( ) = =
= = 229
81 81 9
625 625 5 125
12
34 4
33
613
6
3.
4.
5.
= =
= ( ) = =
( ) =X X(( )
= =
( ) = =
13
63 2
12
17 1
217
X X
Y Y Y6.11
14 14
4 615 4 6
15 10
15
10 1
or Y
Y Y Y Y
Y
7. ⋅( ) = ( ) = ( ) =+
( )(55 105 2
23 3
22
14
51 1
4
27 27 3 9
81 81
) = =
= ( ) = =
( ) =
Y Y
8.
9.
= = ( ) =
=
⋅ =
51
54 4
5
5
13
13 3
81 81
3 243
64 64 6410. ⋅⋅ = ⋅ =
( ) = =
64 4 4 16
16 16 16
3
13
34 1
334
1411. == =
⋅( ) = ( ) = ( ) =
=
+
( )
16 24
3 514 3 5
14 8
14
8 14
8
12. X X X X
X X( ) 44 2
12
34
41 1
234
41 2
434
41
54
=
⋅( ) = ( ) = ( ) =
( )+ +
X
Y Y Y Y
Y
13.441 5
441 5
313 4
15 3
= =
( ) ⋅
=
Y Y
X X X14.(( )
+
⋅
=
⋅ = =
13 4
15
1 415 1 4
15
X
X X X X5515
5 15 1
435
16
4
= = =
( )
=
( )
(
X X X
X X15.))
= =
( )
⋅( )
35
16
1230
25 5
2
6 8
X
X or X
Y Y16.112 6 8
12 14
12
14 12 7
= ( ) = ( ) =
=
+
( )
Y Y
Y Y
Systematic Review 31C
1.
2.
3.
4.
8 8 2
9 9 3
5 5 125
1 000 1 000
13 3
12
31 3
23 3
= =
= =
= =
=, ,22 2
232
2 32
62 3
10 100= =
( ) = = =( )
5. X X X X
aLGeBra 1
sYsteMatic reVieW 31c - sYsteMatic reVieW 31c
soLutions 287
1.
2.
3.
4.
8 8 2
9 9 3
5 5 125
1 000 1 000
13 3
12
31 3
23 3
= =
= =
= =
=, ,22 2
232
2 32
62 3
10 100= =
( ) = = =( )
5. X X X X
6.
7.
2 4 2 2 2 2 2 213
13 2
13
2 13
63
73 3
7
23
⋅ = ⋅ = = = ( )( )
+ +or
Y YY Y Y Y or Y14
23
14
812
312
1112 12
11
145 5
( ) = = = ( )( )
+ +
8.223
14
23
312
812
1112
1211
5 5 5
5
81
2 5
( ) = = =
( )×
+ +
or
in .9.
. .
cmin
cm
qt litersqt
liters
120
301
951
28 5
=
× =10.
111.
12.
72 78 75 75
5 616 5 625
2 1 2002
× < ( )( )<
>
, ,
,mi acrees
mimi mi
21
5 2801
5 2801
55 756 800
2
2
× × =, ft , ft
, , ft
11 2001
43 5601
52 272 000
55 7
22, , ft , , ft
,
acresacre
× =
556 800 52 272 000
2 1 200
2 2
2
, ft , , ft
,
>
>so mi acres
113.
14.
A B A B A B A AB B
X X X Y
+( ) = +( ) +( ) = + +
−( ) + +
2 2 2
2 2
2
2 2(( ) =( ) + +( ) + −( ) + +( ) =
+ + −
X X X Y X X Y
X X XY X
2 2 2 2
3 2 2 2
2 2 2
2 2 −− − =
+ − −
+ + = +( ) +( )
4 2
4 2
11 24 8 3
2
3 2 2
2
X Y
X XY X Y
X X X X15.
16.. − − =+ = −
−( )= −
4 4 20
5
Y X
Y X
Y
divided both sides by 4
55
5 3 10 5 5 3 10
25 5 3 105 3 1
−
+ = => − −( ) + =− − + =
− + =
X
Y X X X
X XX X 00 25
2 35
352
17 12
5 5 352
+− =
= − = −
= − − => = − − −
X
X or X
Y X Y
= − +
=
Y
Y or
102
352
252
12 12
17. Answers for the nnext two questions will vary.
The example given is for the
state of Pennsylvania.
44,832mi
113.
14.
A B A B A B A AB B
X X X Y
= + +
−( ) + +
2 2 2
2 2
2
2 2(( ) =( ) + +( ) + −( ) + +( ) =
+ + −
X X X Y X X Y
X X XY X
2 2 2 2
3 2 2 2
2 2 2
2 2 −− − =
+ − −
+ + = +( ) +( )
4 2
4 2
11 24 8 3
2
3 2 2
2
X Y
X XY X Y
X X X X15.
16.. − − =+ = −
−( )= −
4 4 20
5
Y X
Y X
Y
divided both sides by 4
55
5 3 10 5 5 3 10
25 5 3 105 3 1
−
+ = => − −( ) + =− − + =
− + =
X
Y X X X
X XX X 00 25
2 35
352
17 12
5 5 352
+− =
= − = −
= − − => = − − −
X
X or X
Y X Y
= − +
=
Y
Y or
102
352
252
12 12
17. Answers for the nnext two questions will vary.
The example given is for the
state of Pennsylvania.
44,832mi2
15× ,, ft , ft
, , , ,
2801
5 2801
1 249 844 400 000
mi mi× ≈
(roundedd)
18.
19
1 249 844 400 000
6 000 000 000 208 2
, , , ,
, , , ft
÷
≈
..
20.
452 62 28 024
28 0241
12 000
14
× =
×
,
,,
lb
lb tonlb
≈ ttons
Systematic Review 31D SystematicReview 30D
1.
2.
4 4 2 8
81 81
32 2
33
12
= ( ) = =
= = 99
7 7 49
64 64 4
21 2
13 3
32
12 3
212
3.
4.
5.
= =
= =
( ) =
Y Y
+
= ( )⋅ = ⋅ =
Y or Y34 4
3
13
13 3
13
310 1 000 10 10 10,6. ==
= ( )( )( ) = =
+
+
10 10 1013
93
103 3
10
34
14
34
14
or
A A A A7.444 1
234
2 34
64
32 2 3
5
= =
( ) = = =( )
A A
X X X X or X8.
9. 001
1 61
80
1001
281
2 800
mi kmmi
km
oz goz
g
× =
× =
.
,10.
111.
12.
43 47 45 45
2 021 2 025
25 12 00
× < ( )( )<
<
, ,
. ,acres 00
251
43 5601
10 890
10 8
aLGeBra 1
sYsteMatic reVieW 31e - sYsteMatic reVieW 31e
soLutions288
99
7 7 49
64 64 4
21 2
13 3
32
12 3
212
3.
4.
5.
= =
= =
( ) =
Y Y
+
= ( )⋅ = ⋅ =
Y or Y34 4
3
13
13 3
13
310 1 000 10 10 10,6. ==
= ( )( )( ) = =
+
+
10 10 1013
93
103 3
10
34
14
34
14
or
A A A A7.444 1
234
2 34
64
32 2 3
5
= =
( ) = = =( )
A A
X X X X or X8.
9. 001
1 61
80
1001
281
2 800
mi kmmi
km
oz goz
g
× =
× =
.
,10.
111.
12.
43 47 45 45
2 021 2 025
25 12 00
× < ( )( )<
<
, ,
. ,acres 00
251
43 5601
10 890
10 8
22
ft
. , ft , ft
,
sq
acresacre
× =
990 12 000
2
2 2
2
2
ft , ft<
−( ) = −( ) −( ) =− +
13. X A X A X A
X XA A22
2
2 2
2 2 4
2 4 2 2 4
14. X X X
X X X X X
X
+( ) − +( ) =( ) − +( ) + ( ) − +( ) =
33 2 2 3
2
2 4 2 4 8 8
1 6 7 6
− + + − + = +
−( ) −( ) = − +
X X X X X
X X X X15.
16. XX
Y X YY
Y
= −
− = => − −( ) =+ =
= −
− −( )
4
0 4 04 0
4
4 4
262 400
,
,17. mmi
mimi mi
2
2262 4001
5 2801
5 2801
7 315 2
, , ft , ft
, ,
× × ≈
992 160 000
7 315 292 160 000 6 000 000 0
2, , ft
, , , , , , ,18. ÷ 000
1 219
706 62 43 772
43 7721
1
2≈ , ft
,
,
19.
20.
× =
×
lb
lb ttonlb
ton ton
2 000
43 7722 000
22
,
,,
=
≈
Systematic Review 31ESystematicReview 30E
1.
2.
10 10 10 000
25 25
41 4
32
= =
=
,
(( ) = =
= =
= ( ) = =
(
3 3
44 1
32
3 3
3
5 125
13 13 13
16 16 4 64
3.
4.
5. A )) = = = =
⋅ = ⋅ =
( )
+
13
3 13
33 1
12
12 3
12
33 27 3 3 3
A A A A
6. == =+
+ +
3
3 3
12
62
72
7
56
12
56
12
56
36
SystematicReview 30E
1.
2.
10 10 10 000
25 25
41 4
32
= =
=
,
(( ) = =
= =
= ( ) = =
(
3 3
44 1
32
3 3
3
5 125
13 13 13
16 16 4 64
3.
4.
5. A )) = = = =
⋅ = ⋅ =
( )
+
13
3 13
33 1
12
12 3
12
33 27 3 3 3
A A A A
6. == =
( )( )( ) = = =
+
+ +
3
3 3
12
62
72
7
56
12
56
12
56
36
or
X X X X7. XX
X or X
86
43 3
4
13
12
76
13
12
76
2
2 2 2 2
2
=
( )( )( )( ) =
=
+ +8.
6636
76
126 22 2 4
101
1 11
11
201
+ += = =
× =9.
10.
mm
kg
. yd yd
×× =
× × ×
2 21
44
21
121
121
123
.
ftft ft
lbkg
lb
in in11. iin in
yd
yd yd
13 456
141
31
31
31
3
3
ft,
ft ft ft
=
× × ×12.yyd
A B A B A B
A AB
=
+( ) = +( ) +( )= +
378
5 5 5 5 5 5
25 50
3
2
2
ft
13.
++
−( ) + +( ) =( ) + +( ) + −( ) +
25 2
2 2
2 2 2
B
X Y X XY Y
X X XY Y Y X X
14.
YY Y
X X Y XY X Y XY Y X Y
X X
+( ) =+ + − − − = −
+( ) +
2
3 2 2 2 2 3 3 3
1 4 615. (( ) = + ++ = => = −
−( ) − = −( ) =>
4 10 6
6 2 2 6
3 2 6
3
2X X
Y X Y X
Y X
Y
16.
−− =− + =
=
=
=
= − => = ( ) −
4 2
3 6 182 20
202
10
2 6 2 10 6
X
Y XX
X
X
Y X Y
Y == −=
( )
20 614
10 14
586 400
586 40
Y
square miles
,
,
,
17.
001
5 2801
5 2801
16 347 893 760 0
2mimi mi
× ×, ft , ft
, , , ,
≈
000
16 347 893 760 000 6 000 000 000
2 72
2ft
, , , , , , ,
,
18. ÷
≈ 44 6
100 100 50 500 000
500 000 62 31
2
3
. ft
, ft
, ,
19. × × =× =
aLGeBra 1
sYsteMatic reVieW 31e - Lesson Practice 32B
soLutions 289
−− =− + =
=
=
=
= − => = ( ) −
4 2
3 6 182 20
202
10
2 6 2 10 6
X
Y XX
X
X
Y X Y
Y == −=
( )
20 614
10 14
586 400
586 40
Y
square miles
,
,
,
17.
001
5 2801
5 2801
16 347 893 760 0
2mimi mi
× ×, ft , ft
, , , ,
≈
000
16 347 893 760 000 6 000 000 000
2 72
2ft
, , , , , , ,
,
18. ÷
≈ 44 6
100 100 50 500 000
500 000 62 31
2
3
. ft
, ft
, ,
19. × × =× = 0000 000
31 000 0001
12 000
31 000
,
, ,,
,
lb
lb tonlb
20. × =
,,,
,0002 000
15 500ton tons=
Lesson Practice 32ALessonPractice 31A1.
2.
500 000 5 10
356 000 000
5,
, ,
= ×
== ×
= ×
= × −
3 56 10
54 800 000 5 48 10
00096 9 6 10
8
7
.
, , .
. .
3.
4. 44
3
8
00468 4 68 10
0000000913 9 13 10
20
5.
6.
7.
. .
. .
= ×
= ×
−
−
00 000 6 000 000
1 200 000 000 000
1 9 10 6 105
, , ,
, , , ,
.
× =
×( ) × 66
5 6
11 12
1 9 6 10 10
11 4 10 1 10
( ) =×( ) ×( ) =× ×
.
. ≈ 1 SD (siignificant digit)
8. 200 000 4 000 000 000
800 0
, , , ,
,
× =000 000 000 000
1 815 10 4 16 10
1 815 4 16
5 9
, , ,
. .
. .
×( ) ×( ) =×(( ) ×( ) =× × ( )
10 10
7 5504 10 7 55 10 3
900
5 9
14 14. .
,
≈ SD
9. 0000 40 000 000
36 000 000 000 000
8 6 10 3 645
× =
×( )
, ,
, , , ,
. . ××( ) =×( ) ×( ) =
× ×
10
8 6 3 64 10 10
31 304 10 3 1 10
7
5 7
12 1
. .
. .≈ 33
5
2
00009 9 000 000 000 810 000
8 5 10
. , , , ,
.
SD( )× =
× −
10.
(( ) ×( ) =×( ) ×( ) = × =
×
−
9 10
8 5 9 10 10 76 5 10
7 65 10
9
5 9 4
5
. .
. ≈ 88 10 1
0009 50 000 45
9 3 10 5 10
5
4 4
× ( )× =
×( ) ×(−
. ,
.
SD
11.
)) =×( ) ×( ) =× = × ×
−9 3 5 10 10
46 5 10 4 65 10 5 10 1
4 4
0 1 1
.
. . ≈ SDD( )× =
×( ) ×( )− −
12. . . .
. .
002 0004 0000008
2 1 10 3 50 103 4 ==
×( ) ×( ) =× ×
− −
− −
2 1 3 50 10 10
7 35 10 7 4 10 2
3 4
7 7
. .
. .≈ SD
=
×( ) ×( ) =× ×
10
8 6 3 64 10 10
31 304 10 3 1 10
7
5 7
12 1
. .
. .≈ 33
5
2
00009 9 000 000 000 810 000
8 5 10
. , , , ,
.
SD( )× =
× −
10.
(( ) ×( ) =×( ) ×( ) = × =
×
−
9 10
8 5 9 10 10 76 5 10
7 65 10
9
5 9 4
5
. .
. ≈ 88 10 1
0009 50 000 45
9 3 10 5 10
5
4 4
× ( )× =
×( ) ×(−
. ,
.
SD
11.
)) =×( ) ×( ) =× = × ×
−9 3 5 10 10
46 5 10 4 65 10 5 10 1
4 4
0 1 1
.
. . ≈ SDD( )× =
×( ) ×( )− −
12. . . .
. .
002 0004 0000008
2 1 10 3 50 103 4 ==
×( ) ×( ) =× × (
− −
− −
2 1 3 50 10 10
7 35 10 7 4 10 2
3 4
7 7
. .
. .≈ SD))=
×( ) ×
13. 600 000 4 000 000 000 00015
5 6 10 4 105
, , , , .
.
÷
÷ 99
5 9 4 45 6 4 10 10 1 4 10 1 10 1
( ) =( )( ) = × × ( )− −. .÷ ÷ ≈ SD
14. 110 000 0002 000 000
5
9 8 10 2 45 10
9 8
6 6
, ,, ,
. .
.
=
×( ) ×( ) =÷
÷22 45 10 10 4 0 10 4 0 2
004
6 6 0. . .
. .
( )( ) = × ( )÷
÷
or SD
15. 001 4
3 6 10 1 2 10
3 6 1 2 10 10
3 2
3 2
=
×( ) ×( ) =( )(
− −
− −
.
. .
. .
÷
÷ ÷ )) = × ( )−3 0 10 21. SD
Lesson Practice 32BLessonPractice 31B1.
2.
600 000 6 10
854 000 000
5,
, ,
= ×
== ×
= ×
= ×
8 54 10
62 800 000 6 28 10
000095 9 5 10
8
7
.
, , .
. .
3.
4. −−
−
−
= ×
= ×
5
3
7
00528 5 28 10
000000921 9 21 10
20
5.
6.
7.
. .
. .
00 000 5 000 000
1 000 000 000 000
1 8 10 5 105
, , ,
, , , ,
.
× =
×( ) × 66
5 6 111 8 5 10 10 9 10 1
900 000 3 0
( ) =×( ) ×( ) = × ( )
×.
, ,
SD
8. 000 000 2 700 000 000 000
9 15 10 3 10 9 155 6
, , , , ,
. .
=
×( ) ×( ) = ××( ) ×( ) =× = × ×
3 10 10
27 45 10 2 745 10 3 10 1
5 6
11 12 12. . ≈ SD(( )× =9. 100 000 40 000 000
4 000 000 00
, , ,
, , , 00 000
9 6 10 4 36 10
9 6 4 36 10
4 7
4
,
. .
. .
×( ) ×( ) =×( ) ××( ) =
× = ×
×
10
41 856 10 4 1856 10
4 2
7
11 12. .
. ≈ 110 2
00008 9 000 000 000 720 000
7 5 1
12
. , , , ,
.
SD( )× =
×
10.
00 9 10
7 5 9 10 10
67 5 10 6 75 1
5 9
5 9
4
−
−
( ) ×( ) =×( ) ×( ) =× = ×
.
. . 00 7 10 1
00008 60 000 4 8
7 9 10 6
5 5
5
≈ × ( )× =
×( )−
. , .
. .
SD
11.
225 10
49 375 10 4 9375 10
4 9 10 4 9
4
1 0
0
×( ) =× = ×
×
aLGeBra 1
Lesson Practice 32B - Lesson Practice 32B
soLutions290
. .
. .
00 000 5 000 000
1 000 000 000 000
1 8 10 5 105
, , ,
, , , ,
.
× =
×( ) × 66
5 6 111 8 5 10 10 9 10 1
900 000 3 0
( ) =×( ) ×( ) = × ( )
×.
, ,
SD
8. 000 000 2 700 000 000 000
9 15 10 3 10 9 155 6
, , , , ,
. .
=
×( ) ×( ) = ××( ) ×( ) =× = × ×
3 10 10
27 45 10 2 745 10 3 10 1
5 6
11 12 12. . ≈ SD(( )× =9. 100 000 40 000 000
4 000 000 00
, , ,
, , , 00 000
9 6 10 4 36 10
9 6 4 36 10
4 7
4
,
. .
. .
×( ) ×( ) =×( ) ××( ) =
× = ×
×
10
41 856 10 4 1856 10
4 2
7
11 12. .
. ≈ 110 2
00008 9 000 000 000 720 000
7 5 1
12
. , , , ,
.
SD( )× =
×
10.
00 9 10
7 5 9 10 10
67 5 10 6 75 1
5 9
5 9
4
−
−
( ) ×( ) =×( ) ×( ) =× = ×
.
. . 00 7 10 1
00008 60 000 4 8
7 9 10 6
5 5
5
≈ × ( )× =
×( )−
. , .
. .
SD
11.
225 10
49 375 10 4 9375 10
4 9 10 4 9
4
1 0
0
×( ) =× = ×
×
−. .
. .
≈
or
. . .
.
2
0003 0000004 00000000012
3 1 10 4
SD( )× =
×( −
12.
)) ×( ) =×( ) ×( ) =× = ×
−
− −
−
4 10
3 1 4 10 10
12 4 10 1 24 1
7
4 7
11
.
. . 00
1 10 1
50 000 40 000 000 00125
5
10
10
−
−× ( )=
≈
÷, , , .
SD
13.
..
.
.
2 10 4 10
5 2 4 10 10
1 3 10 1 1
4 7
4 7
3
×( ) ×( ) =( )( ) =
× ×−
÷
÷ ÷
≈ 00 1
20 000 00060 000 000 000
0003
2 4
3− ( )=
×
, ,, , ,
.
.
SD
14.
110 6 10
2 4 6 10 10
4 10 4 10
7 10
7 10
3
( ) ×( ) =( )( ) =
× = ×− −
÷
÷ ÷.
. 44
4
1
0004 007
3 5 10 7 10
. .
.
SD( )=
×( ) ×− −
15. ÷
÷
0.057142833
4 3 1
2
3 5 7 10 10 5 10
5 10 1
( ) =( )( ) = × =
× ( )− − −
−
. .÷ ÷
SD
Systematic Review 32CSystematicReview 31C1.
2.
700 000 7 10
0076 7 6
5,
. .
= ×
= ××× =
= ×
×
−10
5 000 8 000 000
40 000 000 000 4 10
5
3
10
3. , , ,
, , ,
110 8 10
5 8 10 10 40 10
4 10 1
3 6
3 6 9
10
( ) ×( )×( ) ×( ) = ×
×
4.
5. SDD( )
= = ×
6.
7.
Check with calculator
60 000 100 600 6 1, ÷ 00
6 13 10 1 2 10
6 13 1 2 10 10 5
2
4 2
4 2
. .
. . .
×( ) ×( )( ) ×( ) =
÷
÷8. 1108 102
2
×
×
SystematicReview 31C1.
2.
700 000 7 10
0076 7 6
5,
. .
= ×
= ××× =
= ×
×
−10
5 000 8 000 000
40 000 000 000 4 10
5
3
10
3. , , ,
, , ,
110 8 10
5 8 10 10 40 10
4 10 1
3 6
3 6 9
10
( ) ×( )×( ) ×( ) = ×
×
4.
5. SDD( )
= = ×
6.
7.
Check with calculator
60 000 100 600 6 1, ÷ 00
6 13 10 1 2 10
6 13 1 2 10 10 5
2
4 2
4 2
. .
. . .
×( ) ×( )( ) ×( ) =
÷
÷8. 1108 10
5 1 10 2
2
2
×
× ( )9.
10.
. SD
Check with calculator
111. 1 000 10 10 1 000 10 10
10 10
23 2 3 3
2 2 3
2 2
, ,⋅ ⋅ = ( ) ⋅ ⋅ =
⋅
− −
⋅⋅ = =
⋅ = ( ) ⋅ =
− + + −( )10 10 10 10
8 4 8 2 2
3 2 2 3 1
23 3
22 2
or
12. ⋅⋅ = =
⋅ ⋅ =
⋅ ( ) × =
−
−
2 2 16
10 100 10
10 100 10
1
2 4
13
32 1
13
3 1
13.
00 10 10 10
10 10
13 3 1
13
3 1
13
93
33
7
⋅ × = =
=
− + + −( )
+ + − 33 3
7
51
232
102
12
32
10or
A A A A
( )=
− − + −
+
−14.
=
=
× =
A A
km mikm
miles
g
62 3
101
11 6
6 25
75
15.
16.
..
11035
12 625
3 3 3 3 3 32
× =
−( ) = −( ) −( )
. .ozg
oz
X Y X Y X Y17. ==
− +
+( ) − +( ) =( ) − +( ) +
9 18 92 2
2 2
2 2
X XY Y
X Y X XY Y
X X XY Y
18.
YY X XY Y
X X Y XY X Y XY Y X Y
X X
( ) − +( ) =− + + − + = +
2 2
3 2 2 2 2 3 3 3
19. ++( ) + + = −
+ + + + =
+ + =+( ) +
4 5 3 17
4 5 3 17 0
9 20 0
4 5
2
2
X
X X X
X X
X X(( ) = 0
SystematicReview 31C1.
2.
700 000 7 10
0076 7 6
5,
. .
= ×
= ××× =
= ×
×
−10
5 000 8 000 000
40 000 000 000 4 10
5
3
10
3. , , ,
, , ,
110 8 10
5 8 10 10 40 10
4 10 1
3 6
3 6 9
10
( ) ×( )×( ) ×( ) = ×
×
4.
5. SDD( )
= = ×
6.
7.
Check with calculator
60 000 100 600 6 1, ÷ 00
6 13 10 1 2 10
6 13 1 2 10 10 5
2
4 2
4 2
. .
. . .
×( ) ×( )( ) ×( ) =
÷
÷8. 1108 10
5 1 10 2
2
2
×
× ( )9.
10.
. SD
Check with calculator
111. 1 000 10 10 1 000 10 10
10 10
23 2 3 3
2 2 3
2 2
, ,⋅ ⋅ = ( ) ⋅ ⋅ =
⋅
− −
⋅⋅ = =
⋅ = ( ) ⋅ =
− + + −( )10 10 10 10
8 4 8 2 2
3 2 2 3 1
23 3
22 2
or
12. ⋅⋅ = =
⋅ ⋅ =
⋅ ( ) × =
−
−
2 2 16
10 100 10
10 100 10
1
2 4
13
32 1
13
3 1
13.
00 10 10 10
10 10
13 3 1
13
3 1
13
93
33
7
⋅ × = =
=
− + + −( )
+ + − 33 3
7
51
232
102
12
32
10or
A A A A
( )=
− − + −
+
−14.
=
=
× =
A A
km mikm
miles
g
62 3
101
11 6
6 25
75
15.
16.
..
11035
12 625
3 3 3 3 3 32
× =
−( ) = −( ) −( )
. .ozg
oz
X Y X Y X Y17. ==
− +
+( ) − +( ) =( ) − +( ) +
9 18 92 2
2 2
2 2
X XY Y
X Y X XY Y
X X XY Y
18.
YY X XY Y
X X Y XY X Y XY Y X Y
X X
( ) − +( ) =− + + − + = +
2 2
3 2 2 2 2 3 3 3
19. ++( ) + + = −
+ + + + =
+ + =+( ) +
4 5 3 17
4 5 3 17 0
9 20 0
4 5
2
2
X
X X X
X X
X X(( ) = 0
aLGeBra 1
sYsteMatic reVieW 32D - sYsteMatic reVieW 32D
soLutions 291
X
X
+ == −
4 0
4
X
X
+ == −
5 0
5
Check :
−( ) −( ) +( ) + −( ) + = −−( ) ( ) − + =
4 4 4 5 4 3 17
4 0 20 3 −−− + = −
− = −
17
0 20 3 17
17 17
−( ) −( ) +( ) + −( ) + = −−( ) −( ) − + = −
−
5 5 4 5 5 3 17
5 1 25 3 17
5 225 3 17
17 17
+ = −− = −
20. X X2 9 0−( ) =
X = 02 9 0
2 9
92
X
X
X
− ==
=
Check : 0 2 0 9 0
0 0 9 0
0 9 0
0 0
92
( ) ( ) −( ) =( ) −( ) =( ) −( ) =
=
−
=
−
=
2 92
9 0
92
182
9 0
92
−( ) =
( ) =
=
9 9 0
92
0 0
0 0
Systematic Review 32DSystematicReview 31D1.
2.
586 000 000 5 86 10
0
8, , .
.
= ×
000595 5 95 10
20 000 007 140
1 8 10 7 2 1
4
4
= ×× =
×( ) ×
−.
, .
. .
3.
00
1 8 7 2 10 10 12 96 10
1 296 10
3
4 3 1
−
−
( )×( ) ×( ) = ×
×
4.
5.
. . .
. 22 21 3 10 2
1 000
≈ .
, ,
× ( )SD
6.
7.
Check with calculator
0000 300 3 333 3
1 45 10 2 9 10
1 45 2 9
6 2
÷
÷
÷
=
×( ) ×( )(
, .
. .
. .8. ))( ) = ×
× ( )10 10 5 10
5 0 10 2
6 2 4
3
÷ .
.9.
10.
SD
Check with ccalculator
1.
2.
586 000 000 5 86 10
0
, , .
. 000595 5 95 10
20 000 007 140
1 8 10 7 2 1
4
4
= ×× =
×( ) ×
−.
, .
. .
3.
00
1 8 7 2 10 10 12 96 10
1 296 10
3
4 3 1
−
−
( )×( ) ×( ) = ×
×
4.
5.
. . .
. 22 21 3 10 2
1 000
≈ .
, ,
× ( )SD
6.
7.
Check with calculator
0000 300 3 333 3
1 45 10 2 9 10
1 45 2 9
6 2
÷
÷
÷
=
×( ) ×( )(
, .
. .
. .8. ))( ) = ×
× ( )10 10 5 10
5 0 10 2
6 2 4
3
÷ .
.9.
10.
SD
Check with ccalculator
11. 5 5 5 5 5
5 5 5
12
4
0 212
40 2
2 2 2 2
( ) = =
=
−
−( )
+
− − +
== =
⋅ ⋅ = ( ) ⋅ ⋅ ( ) =
⋅ ⋅ =
5 1
9 27 81 9 3 81
3 3 3 3
0
32
14
33 4
1
3 3 1 3
12.++ + =3 1 73 2 187,or
13. 261
1 61
41 6mi kmmi
km× =. .
14.500
1035
117 5
g ozg
oz× =. .
15. D D D
D D D D D
−( ) + +( ) =( ) + +( ) + −( ) + +( )
5 5 25
5 25 5 5 25
2
2 2 ==
+ + − − − =
−
D D D D D
D
3 2 2
3
5 25 5 25 125
125
16. A AT T
A T A A A T
A A T
A T A
A
2 2
3 2 3
3 2
2
2
0 0
0
− +
+ + + +
− +( )− +
− − TT AT
AT T
AT T
−( )+
− +( )
2
2 3
2 3
0
17. X X5 10 0−( ) =X = 05 10 0
5 10
105
2
X
X
X
− ==
= =
0 5 0 10 0 2 5 2 10 0
0 0 10 0
( ) ( ) −( ) = ( ) ( ) −( ) =( ) −( ) =
2 10 10 0
0 10 0 2
( ) −( ) =( ) −( ) = ( ))( ) =
= =0 0
0 0 0 0
aLGeBra 1
sYsteMatic reVieW 32D - sYsteMatic reVieW 32e
soLutions292
18. X X
X X
X X
2 7 18 42
2 7 60 0
12 5 0
+ − =
+ − =+( ) −( ) =
X
X
+ == −
12 0
12
X
X
− ==
5 0
5
−( ) + −( ) − =− − =
=
122
7 12 18 42
144 84 18 42
42 42
52
7 5 18 42
25 35 18 42
42 42
( ) + ( ) − =+ − =
=19.
10 2 2 4 4 8 3 4 11
10 2 4 4
N N N N
N N N
( ) + +( ) − +( ) + = +( ) −+ + − −116 8 3 12 11
10 2 4 3 12 11 4 16 85 5
+ = + −
+ − − = − − + −=
N
N N N NNN == 1
1 3 5; ;
20.
. . .10 05 1 35 100
16 5
10 5 13D N
D N
D N+ =( )( )+ =( ) −( )
+ = 555 5 805 55
555
11
16 11 1616
− − = −=
=
=
+ = ( ) + == −
D ND
D
D
D N NN 111
5N =
Systematic Review 32ESystematicReview 31E1.
2.
23 800 000 2 38 10
00
7, , .
.
= ×
00000112 1 12 10
9 600 000 540 000
9 2 10
7
1
= ×× =
×(
−
−
.
. , ,
.
3.
)) ×( )×( ) ×( ) = ×−
6 4 10
9 2 6 4 10 10 58 88 10
5 8
5
1 5 4
.
. . .
.
4.
5. 888 10 5 9 10 25 5× × ( )≈ .
.
SD
6.
7.
Check with calculator
44 3 001 120
4 10 2 5 10 1 10
4 2
1 1 3
× =
×( ) ×( ) ×( )×
− − −
. .
.
.
÷
÷
8. 55 1 10 10 10 10 10
1 10 1
1 1 3 1
2
÷ ÷( ) ×( ) = ×
× ( )− − −
9.
10.
SD
Cheeck with calculator
00000112 1 12 10
9 600 000 540 000
9 2 10
= ×× =
×(
.
. , ,
. )) ×( )×( ) ×( ) = ×−
6 4 10
9 2 6 4 10 10 58 88 10
5 8
5
1 5 4
.
. . .
.
4.
5. 888 10 5 9 10 25 5× × ( )≈ .
.
SD
6.
7.
Check with calculator
44 3 001 120
4 10 2 5 10 1 10
4 2
1 1 3
× =
×( ) ×( ) ×( )×
− − −
. .
.
.
÷
÷
8. 55 1 10 10 10 10 10
1 10 1
1 1 3 1
2
÷ ÷( ) ×( ) = ×
× ( )− − −
9.
10.
SD
Cheeck with calculator
11.
12.
A A A A A
or A
34
43
34
43
912
1612
2512
1225
9
= = =
( )
+ +
112 2
43 2 3
4
1 2 4 1 2 4 7
3 27 9 3 27
3 3 3 3 3
⋅ ⋅ = ( ) ⋅ ⋅ ( ) =
⋅ ⋅ = =+ +
13. 11001
1 11
110
21
1 061
mm
liters qtliter
× =
×
. yd yd
.14. ==
− = −( ) +( )
2 12
2 2
. qt
X B X B X B15.
16. 4 324 4 81
4 9 9
4
5 4
2 2
X X X X
X X X
X X
− = ( ) −( ) =( ) −( ) +( ) =( ) −33 3 9
12 60
72 0
9 8
2
2
2
( ) +( ) +( )+ − =+ − =
+( ) −( )
X X
X X
X X
X X
17.
== 0
X
X
+ == −
9 0
9
X
X
X
X
+ == −
− ==
9 0
9
8 0
8
−( ) −( ) − = ( ) + ( ) − =− − =
9 + 9 12 60
28 8 12 60
81 9 12 60
2
64 8 12 60
60 60 60 60
+ − == =
18. 4 0
2 2 0
2− =−( ) +( ) =
A
A A
2 0
2
− ==
A
A
2 0
2
+ == −
A
A
4 22
0
4 4 0
− ( ) =− =
4 22
0
4 4 0
0 0
− −( ) =− =
=
aLGeBra 1
sYsteMatic reVieW 32e - Lesson Practice 33a
soLutions 293
19. 9 5 10
9 5 101
5 28 101
6
6 2 3
.
. . ft
×
× × ×
square miles
mimmi mi
sq
× × =
× ×
5 28 101
2 6 10
2
3
14
. ft
. ft264.8448 1012 ≈
SD( )Your answer may be slightly
different, deppending on how many
significant digits were givven by the
source of information that you
used,, and the point at which you
rounded.
20.
2 65 1. × 00 6 10
2 65 6 10 10
14 9
14 9
ft
.
sq people( ) ×( ) =( )( ) =
÷
÷ ÷ ..
. ft
.
44 10
4 4 10 4 10
1 4 4
5
4 4 2
× =
× ×≈
≈
per person
acre ××104 2ft
so 1 acre per person
Your answer to thiis problem will
be affected by the answer to thhe
previous problem. As long as
yours is close to the one given
here, it can be counted correect.
Lesson Practice 33A1. 3
27 3 9
3
2
is the largest power of 3 ≤ 80
33 = =; ; ;3 3 3 1
2
27 8054
26
2
9 2618
8
2
3 86
2
2
1 22
0
2 3
1 0
3
= =
× +22 3 2 3 2 3 22222 1 03× + × + × =
2. 5
25 5 5
2
1; ;
is the largest power of 5 ≤ 80
52 = = 5 1
25 8075
5
1
5 55
0
0
1 00
0
3 5 1 5 0 5 310
0
2 1 05
=
× + × + × =
3
3. 4
64 4 16
3
2
is the largest power of 4 ≤ 80
43 = =; ;; ;4 4 4 1
1
64 8064
16
1
16 1616
0
0
4 00
0
0
1 00
0
1 4
1 0= =
× 33 2 1 041 4 0 4 0 4 1100+ × + × + × =
4. 6
36 6 6
2
1
is the largest power of 6 ≤ 100
62 = =; ;; 6 1
2
36 10072
28
4
6 2824
4
4
1 44
0
2 6 4 6 4 6
0
2 1 0
=
× + × + × = 22446
5. 8
512 8
3 is the largest power of 8 ≤ 1,352
83 = ; 22 1 064 8 8 8 1
2
512 13521024
328
5
64 328320
8
1
8
= = =; ;
888
0
0
1 00
0
2 8 5 8 1 8 0 8 25103 2 1 08× + × + × + × =
6. 6
1 296
4 is the largest power of 6 ≤ 1,352
64 = , ; ; ;
;
6 216 6 36 6
6 6 1
1
1296 13521296
56
0
216
3 2 1
0
= = =
=
560
56
1
36 5636
20
3
6 20
18
2
2
1 22
0
1 6 0 6 1 6 34 3 2× + × + × + ×× + × =6 2 6
10132
1 0
6
7. 563 5 7 6 7 3 7
5 49 6 7 3 1
245 42 3
72 1 0= × + × + × =
( ) + ( ) + ( ) =+ + = 2290
aLGeBra 1
Lesson Practice 33a - Lesson Practice 33B
soLutions294
8. 4415 4 52 4 51 1 50
4 25 4 5 1 1
100 2
= × + × + × =
( ) + ( ) + ( ) =+ 00 1 121+ =
9. 21213 2 33 1 32 2 31 1 30
2 27 1 9 2 3
= × + × + × + × =
( ) + ( ) + ( ) ++ ( ) =+ + + =
1 1
54 9 6 1 70
10. 3421 3 5 4 5 2 5 1 5
3 125 4 25 2 55
3 2 1 0= × + × + × + × =
( ) + ( ) + ( ) +111
375 100 10 1 486
6 8 6 12 10 12 8 1122 1
( ) =+ + + =
= × + × + ×11. A 22
6 144 10 12 8 1
864 120 8 992
81 11
0
13
=( ) + ( ) + ( ) =
+ + =
=12. B ×× + × + × =
( ) + ( ) + ( ) =+ +
13 8 13 1 13
11169 8 13 11
1 859 104
2 1 0
, 11 1 964= ,
Lesson Practice 33B1. 2
64 2 32
6
5
is the largest power of 2 ≤ 95
26 = =; ;; ; ;
; ;
2 16 2 8
2 4 2 2 2 1
1
64 9564
31
0
32 31
4 3
2 1 0
= =
= = =
00
31
1
16 3116
15
1
8 1587
1
4 74
3
1
2 32
1
1
1 11
0
1 2 0 26× + × 55 4 3 2
1 02
1 2 1 2 1 2
1 2 1 2 1011111
+ × + × + × +
× + × =
2. 5
25 5 5
2
1
is the largest power of 5 ≤ 95
52 = =; ; 5 1
3
25 9575
20
4
5 2020
0
0
1 00
0
3 5 4 5 0 5 34
0
2 1 0
=
× + × + × = 005
3. 7
49 7 7
2
1
is the largest power of 7 ≤ 95
72 = =; ; 7 1
1
49 9549
46
6
7 4642
4
4
1 44
0
1 7 6 7 4 7 16
0
2 1 0
=
× + × + × = 447
4. 8
64 8 8
2
1
is the largest power of 8 ≤ 100
82 = =; ;; 8 1
1
64 10064
36
4
8 3632
4
4
1 44
0
1 8 4 8 4 8
0
2 1 0
=
× + × + × = 11448
5. 12
12 144
2
2
is the largest power
of 12 ≤ 1,352
= ;; ;12 12 12 1
9
144 13521296
56
4
12 5648
8
8
1 88
0
9
1 0= =
×× + × + × =12 4 12 8 12 948
9
2 1 012
36. is the largest powerr
of 9 ≤ 1,352
93 = = = =729 9 81 9 9 9 1
1
729 13
2 1 0; ; ;
552729
623
7
81 623567
56
6
9 5654
2
2
1 22
0
1 9 7 9 63 2× + × + ×99 2 9 1762
11001
1 2 1 2 0 2 0 2 1 2
1 09
24 3 2 1 0
+ × =
=
× + × + × + × + ×
7.
==( ) + ( ) + ( ) + ( ) + ( ) =+ + + + =
116 1 8 0 4 0 2 11
16 8 0 0 1 25
2121
aLGeBra 1
Lesson Practice 33B - sYsteM reVieW 33c
soLutions 295
12
12 144
2
2 = ;; ;12 12 12 1
9
144 13521296
56
4
12 5648
8
8
1 88
0
9
1 0= =
×× + × + × =12 4 12 8 12 948
9
2 1 012
36. is the largest powerr
of 9 ≤ 1,352
93 = = = =729 9 81 9 9 9 1
1
729 13
2 1 0; ; ;
552729
623
7
81 623567
56
6
9 5654
2
2
1 22
0
1 9 7 9 63 2× + × + ×99 2 9 1762
11001
1 2 1 2 0 2 0 2 1 2
1 09
24 3 2 1 0
+ × =
=
× + × + × + × + ×
7.
==( ) + ( ) + ( ) + ( ) + ( ) =+ + + + =
116 1 8 0 4 0 2 11
16 8 0 0 1 25
21218. 773 2 1 02 7 1 7 2 7 1 7
2 343 1 49 2 7 11
6
=
× + × + × + × =( ) + ( ) + ( ) + ( ) =886 49 14 1 750
465 4 7 6 7 5 7
4 49 6 77
2 1 0
+ + + =
= × + × + × =
( ) + ( )9.
++ ( ) =+ + =
=
× + × + × + ×
5 1
196 42 5 243
3421
3 6 4 6 2 6 1 6
63 2 1 0
10.
==( ) + ( ) + ( ) + ( ) =
+ + + =3 216 4 36 2 6 11
648 144 12 1 805
2611. A1122 1 02 12 6 12 10 12
2 144 6 12 10 1 288 7
= × + × + × =( ) + ( ) + ( ) = + 22 10 370
3 4 3 20 11 20 4 20
3 400 11 220
2 1 0
+ =
= × + × + × =
( ) +12. B
00 4 1
1 200 220 4 1 424
( ) + ( ) =+ + =, ,
System Review 33CSystematicReview 32C1. 34 is the largest power
oof 3 ≤ 100
34 = = =
= =
81 3 27 3 9
3 3 3 1
1
81 10
3 2
1 0
; ; ;
;
008119
0
27 190
19
2
9 1918
1
0
8 101
1
1 110
1 3 0 34 3× + × +22 3 0 3 1 3 102012 1 03× + × + × =
2. 6
216 6
3
2
is the largest power of 6 ≤ 245
63 = =; 336 6 6 6 1
1
216 24521629
0
36 290
29
4
6 2924
5
5
1
1 0; ;= =
550
1 6 0 6 4 6 5 6 10453 2 1 06× + × + × + × =
3.
4.
56 5 7 6 7
5 7 6 1 35 6 41
173 1 8 7
71 0
82
= × + × =( ) + ( ) = + =
= × + ×88 3 8
1 64 7 8 3 1 64 56 3 123
1 0+ × =
( ) + ( ) + ( ) = + + =
5. 300 7 000 8
3 10 7 10 8 10
3 7 8 10
2 3 1
× × =
×( ) ×( ) ×( ) =× ×( )
−
, .
22 3 1
4 6 6
10 10
168 10 1 68 10 2 10 1
60
× ×( ) =× = × × ( )
×
−
. ≈ SD
6. .. ,05 40 000
6 10 5 10 4 10
6 5 4 10 1
1 2 4
1
× =
×( ) ×( ) ×( ) =× ×( ) ×
−
00 10
120 10 1 2 10 1 10 1
2 4
3 5 5
− ×( ) =× = × × ( ). ≈ SD
aLGeBra 1
sYsteM reVieW 33c - sYsteMatic reVieW 33D
soLutions296
7. 9 000 04300 000 2
9 10 4 10
3 10 2 1
3 2
5, .
, .××
= ×( ) ×( )×( ) ×
−
00
36 10
6 106 10
1 4 005350 000
1 4
1
1
43
−
−
( ) =
××
= ×
× =(
8. . .,
. )) ×( )×( ) =
××
= ×
−
− −
5 10
3 5 10
7 10
3 5 102 10
3
5
3
58
.
.
9. [ ] ( )10 10 10 1212
0 2 12
0 0( ) = = =( ) ( )
10. 4 16 64 4 2 2
2 2 2
32 2
23
34
26
23
3 4 2 6
⋅ ⋅ = ( ) ⋅ ( ) ⋅ ( ) =
⋅ ⋅×( )( 22
3 3 8 4
3 8 4 15
2 2 2
2 2 32 768
)
,
= ⋅ ⋅ =
=+ + or
11. 100 10 10 10
10 10
32 2
42
32 2
4
2 32
⋅ ( ) = ( ) ⋅ ( ) =
⋅( )
22 4 3 8
3 8 11
13 6
23
13
6
10 10
10 10
( )( )
+
− − +
= ⋅ =
=
⋅ ⋅ =12. D D D D++ − + +
= =
× =
23
13
183
23
193
880
191
792
D D
myd
m13.
14.
yd .
AAnswers will vary:
multiply your weight by .45 kg
Answers
15.
16.
4
195
13 8
qt litersqt
liters× =. .
wwill vary: multiply your
weight in kg # 14 b( ) yy 1,000 g
17.
1 24 101
5 28 101
5 28 106 2 3. . ft .× × × × ×mimi
33
12 13 2
13
1
34 6 10 3 46 10
3 46 10
ft
. . ft
.
mi
sq
= × = ×
×
18.
fft
. .
( ) ×( ) =( )( ) = ×
÷
÷ ÷
6 10
3 46 6 10 10 577 10
9
13 9
people
44
3 2
2 2
5 77 10
=
×
− = −( ) +( ). ft per person
B A B A B A19.
20.. C D C D C D
C D C D C D
4 4 2 2 2 2
2 2
− = −( ) +( ) =−( ) +( ) +( )
Systematic Review 33DSystematicReview 32D1. 72 is the smallest power of 7 ≤ 100
72 = = =49 7 7 7 1
2
49 10098
2
0
7 20
2
2
1
1 0; ;
22
0
2 7 0 7 2 7 2022 1 07× + × + × =
2. 82
64
is the smallest power
of 8
2
≤ 245
8 = ; ;81 8 80 1
3
64 245192
53
6
8 5348
5
5
1 55
0
3 82
= =
× + 66 81 5 80 365821203
2 33 1 32 2 31 0 30
× + × =
=
× + × + × + × =
3.
22 27 1 9 2 3 0 1
54 9 6 0 69
32104
3
( ) + ( ) + ( ) + ( ) =+ + + =
=
×
4.
443 2 42 1 41 0 40
3 64 2 16 1 4 0 1
19
+ × + × + × =( ) + ( ) + ( ) + ( ) =22 32 4 0 228
032 8 000 7
3 2 10 2 8 10
+ + + =× × =
× −( ) ×
5. . , .
. 33 7 10 1
3 2 8 7 10 2 103 10 1
179 2
( ) × −( ) =
× ×( ) − × × −( ) =.
. ×× = × ≈
× ( )100 1 792 102
2 102 1
.
SD
2. 82
64
is the smallest power
of 8
2
≤ 245
8 = ; ;81 8 80 1
3
64 245192
53
6
8 5348
5
5
1 55
0
3 82
= =
× + 66 81 5 80 365821203
2 33 1 32 2 31 0 30
× + × =
=
× + × + × + × =
3.
22 27 1 9 2 3 0 1
54 9 6 0 69
32104
3
( ) + ( ) + ( ) + ( ) =+ + + =
=
×
4.
443 2 42 1 41 0 40
3 64 2 16 1 4 0 1
19
+ × + × + × =( ) + ( ) + ( ) + ( ) =22 32 4 0 228
032 8 000 7
3 2 10 2 8 10
+ + + =× × =
× −( ) ×
5. . , .
. 33 7 10 1
3 2 8 7 10 2 103 10 1
179 2
( ) × −( ) =
× ×( ) − × × −( ) =.
. ×× = × ≈
× ( )100 1 792 102
2 102 1
.
SD
6. .003 500 3 10 5 10
3 5 10 10 15 1
3 2
3 2
× = ×( ) ×( ) =×( ) ×( ) = ×
−
− 00 1 5 10
2 10 2 1
12 400 04 1 24
1 0
0
− = ×
× ( )=
.
, . .
≈
÷
or SD
7. ××( ) ×( ) =( )( ) = × =
−
−
10 4 10
1 24 4 10 10 31 10
3 1
4 2
4 2 6
÷
÷ ÷. .
. ×× × ( )= ×( )
10 3 10 1
1 000 000 5 000 000 1 10
5 5
6
≈
÷, , , ,
SD
8. ÷÷
÷ ÷
5 10
1 5 10 10 2 10 2 10 1
6
6 6 0 1
×( ) =( )( ) = × = × ( )−. SD
aLGeBra 1
sYsteMatic reVieW 33D - sYsteMatic reVieW 33e
soLutions 297
9.
10.
8 8 2 1643 3
44
43
12 4
312
= ( ) = =
( ) = =
X X X
446
23= X
11. A A A A A
A A A
− − − + + −( )+
− + − + −
= =
= =
5 4 312
5 4 3 12
4 12
82
12
722
5 2
3 75 3 2 7 2 7 5 3
9 8
12. B A
B AB B A A A B
A B o
−
−− − − + −( ) +
−
= = =
rr B
A
8
9
13. 2 0001
45
1900, .lb kg
lbkg× =
14.
15.
41
121
121
576
2 211
1 5
22ft
ft ft
. .
× × =
=
in in in
E22 2 11 1 5
2 2 16 5
16 52 2
7 5
. .
. .
..
.
E
E
E
AB
CD
AD BC
= ×=
= =
=
=
16.
AADC
B
mi
mi mi
=
× × × × × =17. . . .3 69 101
5 28 101
5 28 101
6 2 3 3
1103 10 1 03 10
1 03 10 6 10
12 14 2
14 2 9
× = ×
×( ) ×
. ft
. ft18. ÷
. .
.
people( ) =( )( ) = × =
×
1 03 6 10 10 172 10
1 72 10
14 9 5
4
÷ ÷
ft per person2
4
41 72 10
4 4 101 72 4 4 1019. .
.. .×
×= ( )÷ 44 4
0 1
10
39 10 3 9 10
÷( ) =× = × −. .
or .39 acres per persoon
20. 5 4 10
5 4 10
45
105
45
2
Y X
Y X
Y X
Y X
+ ≥≥ − +
≥ − +
≥ − +
See graph..
19.
20.
�sq�ft
1.03
× sq ft per person
1.72 × 104
4.4 × 104= 1.72 ÷ 4.4( ) 104 ÷ 104( ) =
.39 × 100 = 3.9 × 10−1
or .39 acres per person
Y
X
Systematic Review 33E1. 9
81 9 9
2
1
is the largest power of 9 ≤ 100
92 = =; ;; 9 1
1
81 10081
19
2
9 1918
1
1
1 11
0
1 9 2 9 1 9
0
2 1 0
=
× + × + × = 11219
2. 4
64 4 1
3
2
is the largest power of 4 ≤ 245
43 = =; 66 4 4 4 1
3
64 245192
53
3
16 5348
5
1
4 54
1
1
1 11
0
1 0; ;= =
33 4 3 4 1 4 1 4 33113 2 1 04× + × + × + × =
3. 35 3 12 5 12 10 12 11 12
3 1 728 5 1412
3 2 1 0AB = × + × + × + × =
( ) +, 44 10 12 111
5 184 720 120 11 6 035
4045
( ) + ( ) + ( ) =+ + + =
=
, ,
4. 44 5 0 5 4 5
4 25 0 5 4 1 100 0 4 104
60
2 1 0× + × + × =
( ) + ( ) + ( ) = + + =5. ,, , .
. .
. .
200 000 507
6 02 10 5 07 10
6 02 5 07
7 1
× =
×( ) ×( ) =×(
−
)) ×( ) =× = × ( )×
−10 10
30 5 10 3 05 10 3
2 000 5
7 1
6 7. .
, ,
SD
6. 0000 400
2 10 5 10 4 10
2 5 4 10 10 1
3 3 2
3 3
× =
×( ) ×( ) ×( ) =× ×( ) × × 00
40 10 4 10 1
90 000 000 000 0000
2
8 9
( ) =× = × ( )
×, , , .
SD
7. 221
9 10 2 1 10
18 9 10 1 89 10
2 10
10 5
5 6
=
×( ) ×( ) =×( ) = ×
×
−.
. . ≈66
4 4 1
1
40 000 30 000 60
4 10 3 10 6 10
, ,
SD( )× =
× × × ×( )8. ÷
÷ ==
×( ) ×( ) =( )( ) = × ( )4 3 6 10 10 10
12 6 10 2 10 1
4 4 1
7 7
÷ ÷
÷ SD
aLGeBra 1
sYsteMatic reVieW 33e - Lesson Practice 34a
soLutions298
,, , .
. .
. .
200 000 507
6 02 10 5 07 10
6 02 5 07
=
×( )) ×( ) =× = × ( )×
10 10
30 5 10 3 05 10 3
2 000 5
7 1
6 7. .
, ,
SD
6. 0000 400
2 10 5 10 4 10
2 5 4 10 10 1
3 3 2
3 3
× =
×( ) ×( ) ×( ) =× ×( ) × × 00
40 10 4 10 1
90 000 000 000 0000
2
8 9
( ) =× = × ( )
×, , , .
SD
7. 221
9 10 2 1 10
18 9 10 1 89 10
2 10
10 5
5 6
=
×( ) ×( ) =×( ) = ×
×
−.
. . ≈66
4 4 1
1
40 000 30 000 60
4 10 3 10 6 10
, ,
SD( )× =
× × × ×( )8. ÷
÷ ==
×( ) ×( ) =( )( ) = × ( )4 3 6 10 10 10
12 6 10 2 10 1
4 4 1
7 7
÷ ÷
÷ SD
9.
10.
X X X X X
X X
25
13
25
13
615
515
1115
25
13 2
( )( ) = = =
( ) =
+ +
5513
215
= X
11.
12.
X X X X X
B BC
23
15
23
15
1015
315
715
6 4
( )( ) = = =− + − + −
−
CC CB B C C C
B C B C or B
C
9 46 1 4 9 4
6 1 4 9 4 7 97
−− −
+ − + −( )+ −
= =
=99
13. 1001
1 61
160mi kmmi
km× =.
14.
15.
14
131
31
31
378
03
33yd ft ft ft ft
.
× × × =yd yd yd
221 5
03 2 1 503 3
303
100
2 2 2
2
=
= ×=
= =
=
.
. .
.
.
WWW
W
XY
X ZA
X
16.
AA YX Z
A YX Z
X
A YZ
=
=
=
2 2
2 2
2
2
17. 3 14 8 0
3 2 4 0
2X X
X X
+ + =+( ) +( ) =
3 2 0
3 2
23
X
X
X
+ == −
= −
X
X
+ == −
4 0
4
3 23
14 23
8 0
3 49
283
8 0
129
2
− + −
+ =
− + =
−− + =
− + =
=
283
243
0
43
283
243
0
0 0
3 4 14 4 8 0
3 16 56 8 0
48 56 8 0
0 0
2−( ) + −( ) + =
( ) − + =− + =
=18.
19.
3 2 9
3 2 9
23
3
23
Y X
Y X
Y X
m S
− == +
= +
=
See graph.
eee graph.
See graph.20. m = − 32
17.
18.
19.
20.
Y
#19
#20
#18
Y=
A
X2A = YX2Z2
A = YX2Z2
X2
A = YZ2
m = − 32�See graph
Lesson Practice 34ALessonPractice 33A1. X Y
Y
YY
2 2
2 2
2
16
0 16
16
+ =
( ) + =
== ±44
aLGeBra 1
Lesson Practice 34a - Lesson Practice 34a
soLutions 299
2.
3.
4.
X Y
X
X
2 2
2 2
16
0 16
4
0 0
16 4
+ =
+ ( ) == ±
( )=
,
Y
X
Y
X
X2 + Y2 = 16
0( )2 + Y2 = 16
Y2 = 16
Y = ±4
X2 + Y2 = 16
X2 + 0( )2 = 16
X = ±4
0,0( )16 = 4
X − 1( )2 + Y − 2( )2 = 9
1( ) − 1( )2 + Y − 2( )2 = 9
02 + Y − 2( )2 = 9
Y − 2( )2 = 9
Y − 2 = ±3
Y − 2 = 3
Y = 5
Y − 2 = −3
Y = −1
5,−1
X − 1( )2 + Y − 2( )2 = 9
X( ) ( )( )2
5. X Y
Y
Y
Y
−( ) + −( ) =
( ) −( ) + −( ) =
+ −( ) =
−
1 2 9
1 1 2 9
0 2 9
2 2
2 2
2 2
22 92 3
2 35
2 31
5 1
2( ) =− = ±
− ==
− = −= −
−
Y
YY
YY
,
6. X Y
X
X
X
−( ) + −( ) =
−( ) + ( ) −( ) =
−( ) + =
−
1 2 9
1 2 2 9
1 0 9
2 2
2 2
2 2
11 91 3
1 34
1 32
4 2
2( ) =− = ±
− ==
− = −= −
−
X
XX
XX
,
7.
8.
9.
1 2
9 3
4 9
4 0 9
93
2 2
2 2
2
,( )=
+ =
( ) + =
== ±
X Y
Y
YY
Y
X
Y
X
X2 + Y2 = 16
0( )2 + Y2 = 16
Y2 = 16
Y = ±4
X2 + Y2 = 16
X2 + 0( )2 = 16
X = ±4
0,0( )16 = 4
X − 1( )2 + Y − 2( )2 = 9
1( ) − 1( )2 + Y − 2( )2 = 9
02 + Y − 2( )2 = 9
Y − 2( )2 = 9
Y − 2 = ±3
Y − 2 = 3
Y
7.
8.
9.
1 2
9 3
4 9
4 0 9
93
2 2
2 2
2
,( )=
+ =
( ) + =
== ±
X Y
Y
YY
9
X − 1( )2 = 9
X − 1= ±3
X − 1= 3
X = 4
X − 1= −3
X = −2
4,−2
1,2( )
Y
X
Y
X
4X2 + Y2 = 9
4X2 + 0( )2 = 9
4X2 = 9
X2 = 94
X = ± 32
Y
6X2 + 4Y2 = 12
6 0( )2 + 4Y2 = 12
4Y2 = 12
Y2 = 3
Y = ± 3
6X2 + 4Y2 = 12
6X2 + 4 0( )2 = 12
6X2 = 12
X2 = 2
X = ± 2
10.
11.
4 9
4 0 9
4 994
32
2 2
2 2
2
2
X Y
X
X
X
X
ellipse
+ =
+ ( ) =
=
=
= ±
12.
13.
6 4 12
6 0 4 12
4 12
3
3
6 4
2 2
2 2
2
2
2
X Y
Y
Y
Y
Y
X
+ =
( ) + =
=== ±
+ YY
X
X
X
X
2
2 2
2
2
12
6 4 0 12
6 12
2
2
=
+ ( ) =
=== ±
14. ellipse
5
Y − 2 = −3
Y = −1
5,−1
X − 1( )2 + Y − 2( )2 = 9
X − 1( )2 + 2( ) − 2( )2 = 9
X − 1( )2 + 02 = 9
X − 1( )2 = 9
X − 1= ±3
X − 1= 3
X = 4
X − 1= −3
X = −2
4,−2
1,2( )
Y
X
Y
X
4X2 + Y2 = 9
4X2 + 0( )2 = 9
4X2 = 9
X2 = 94
X = ± 32
6X2 + 4Y2 = 12
6 0( )2 + 4Y2 = 12
4Y2 = 12
Y2 = 3
Y = ± 3
aLGeBra 1
Lesson Practice 34a - Lesson Practice 34B
soLutions300
15. X Y
Y
YY
and
2 2
2 2
2
25
0 25
255
+ =
( ) + =
== ±
( )Points 0, 5 ,0 5
25
0 25
25
5
2 2
2 2
2
2
−( )+ =
+ ( ) =
== ±
X Y
X
X
X
Points 5, 00
graph
( ) −( ),and
see
5 0
X
Y
X
Y
X
6X2 + 4Y2 = 12
6 0( )2 + 4Y2 = 12
4Y2 = 12
Y2 = 3
Y = ± 3
6X2 + 4Y2 = 12
6X2 + 4 0( )2 = 12
6X2 = 12
X2 = 2
X = ± 2
16. X Y
Y
YY
+( ) + −( ) =
−( ) +( ) + −( ) =
−( ) =−
3 1 4
3 3 1 4
1 41
2 2
2 2
2
== ±
− ==
− = −= −
−( ) −
2
1 23
1 21
3 3
YY
YY
and,Points 33 1
3 1 4
3 1 1 4
3 4
2 2
2 2
2
, −( )+( ) + −( ) =
+( ) + −( ) =
+( ) =
X Y
X
X
X ++ = ±
+ == −
+ = −= −
−( )
3 2
3 21
3 25
1 1
XX
XX
an,Points dd ,−( )5 1
Y
X
Lesson Practice 34BLessonPractice 34B1.
2.
X Y
Y
YY
2 2
2 2
2
4
0 4
42
+ =
( ) + =
== ±
XX Y
X
XX
2 2
2 2
2
4
0 4
42
0 0
4 2
+ =
+ ( ) =
== ±
( )=
3.
4.
,
LessonPractice 34B1.
2.
X Y
Y
YY
2 2
2 2
2
4
0 4
42
+ =
( ) + =
== ±
XX Y
X
XX
2 2
2 2
2
4
0 4
42
0 0
4 2
+ =
+ ( ) =
== ±
( )=
3.
4.
,
Y
X
Y
X
X2 + Y2 = 4
0( )2 + Y2 = 4
Y2 = 4
Y = ±2
X2 + Y2 = 4
X2 + 0( )2 = 4
X2 = 4
X = ±2
0,0( )
4 = 2
5. X Y
Y
YY
+( ) + −( ) =
−( ) +( ) + −( ) =
−( ) =− =
3 4 9
3 3 4 9
4 94
2 2
2 2
2
±±3
Y
Y
− ==
4 3
7
Y
Y
− = −=
4 3
1 7 1,
6. X Y
X
X
X
+( ) + −( ) =
+( ) + ( ) −( ) =
+( ) =+ = ±
3 4 9
3 4 4 9
3 9
3
2 2
2 2
2
33
X
X
+ ==
3 3
0
aLGeBra 1
Lesson Practice 34B - Lesson Practice 34B
soLutions 301
X
X
+ = −= −
−
3 3
6
0 6,
X
X
+ = −= −
−
3 3
6
0 6,
7.
8.
9.
−( )=
+ =
( ) + =
=
=
3 4
9 3
3 2 12
3 0 2 12
2 12
6
2 2
2 2
2
2
,
X Y
Y
Y
Y
YY
X Y
X
X
X
X
X
= ±
+ =
+ ( ) =
=== ±= ±
6
3 2 12
3 2 0 12
3 12
4
4
2 2
2 2
2
2
10.
ellipse
2
5 3 15
5 0 3 15
3 15
2 2
2 2
2
2
11.
12. X Y
Y
Y
Y
+ =
( ) + =
== 55
5
5 3 15
5 3 0 15
5 15
3
3
2 2
2 2
2
2
Y
X Y
X
X
X
X
= ±
+ =
+ ( ) =
=
=
= ±
13.
14.. ellipse
Y
X
= ±
X2 + Y2 = 4
X2 + 0( )2 = 4
X2 = 4
X = ±2
0,0( )
4 = 2
X +3( )2 + Y − 4( )2 = 9
−3( ) +3( )2 + Y − 4( )2 = 9
Y − 4( )2 = 9
Y − 4 = ±3
Y − 4 = 3
Y = 7
Y − 4 = −3
Y = 1
7,1
X +3( )2 + Y − 4( )2 = 9
X +3( )2 + 4( ) − 4( )2 = 9
X +3( )2 = 9
X +3 = ±3
X +3 = 3
X = 0
X +3 = −3
X = −6
0,−6
−3,4( )
9 = 3
3X2 + 2Y2 = 12
3 0( )2 + 2Y2 = 12
2Y2 = 12
Y
Y
X
7.
8.
9.
−( )=
+ =
( ) + =
=
=
3 4
9 3
3 2 12
3 0 2 12
2 12
6
2 2
2 2
2
2
,
X Y
Y
Y
Y
YY
X Y
X
X
X
X
X
= ±
+ =
+ ( ) =
=== ±= ±
6
3 2 12
3 2 0 12
3 12
4
4
2 2
2 2
2
2
10.
ellipse
2
5 3 15
5 0 3 15
3 15
2 2
2 2
2
2
11.
12. X Y
Y
Y
Y
+ =
( ) + =
== 55
5
5 3 15
5 3 0 15
5 15
3
3
2 2
2 2
2
2
Y
X Y
X
X
X
X
= ±
+ =
+ ( ) =
=
=
= ±
13.
14.. ellipse
X
X +3( )2 + Y − 4( )2 = 9
−3( ) +3( )2 + Y − 4( )2 = 9
Y − 4( )2 = 9
Y − 4 = ±3
Y − 4 = 3
Y = 7
Y − 4 = −3
Y = 1
7,1
X +3( )2 + Y − 4( )2 = 9
X +3( )2 + 4( ) − 4( )2 = 9
X +3( )2 = 9
X +3 = ±3
X +3 = 3
X = 0
X +3 = −3
X = −6
0,−6
−3,4( )
9 = 3
3X2 + 2Y2 = 12
3 0( )2 + 2Y2 = 12
2Y2 = 12
Y2 = 6
Y = ± 6
Y
X
Y
3X2 + 2Y2 = 12
3X2 + 2 0( )2 = 12
3X2 = 12
X2 = 4
X = ± 4
7.
8.
9.
−( )=
+ =
( ) + =
=
=
3 4
9 3
3 2 12
3 0 2 12
2 12
6
2 2
2 2
2
2
,
X Y
Y
Y
Y
YY
X Y
X
X
X
X
X
= ±
+ =
+ ( ) =
=== ±= ±
6
3 2 12
3 2 0 12
3 12
4
4
2 2
2 2
2
2
10.
ellipse
2
5 3 15
5 0 3 15
3 15
2 2
2 2
2
2
11.
12. X Y
Y
Y
Y
+ =
( ) + =
== 55
5
5 3 15
5 3 0 15
5 15
3
3
2 2
2 2
2
2
Y
X Y
X
X
X
X
= ±
+ =
+ ( ) =
=
=
= ±
13.
14.. ellipse
ellipse
2
5 3 15
5 0 3 15
3 15
2 2
2 2
2
2
11.
12. X Y
Y
Y
Y
+ =
( ) + =
== 55
5
5 3 15
5 3 0 15
5 15
3
3
2 2
2 2
2
2
Y
X Y
X
X
X
X
= ±
+ =
+ ( ) =
=
=
= ±
13.
14.. ellipse
3
12
3 0( )2 + 2Y2 = 12
2Y2 = 12
Y2 = 6
Y = ± 6
Y
X
3X2 + 2Y2 = 12
3X2 + 2 0( )2 = 12
3X2 = 12
X2 = 4
X = ± 4
5X2 +3Y2 = 15
5 0( )2 +3Y2 = 15
3Y2 = 15
Y2 = 5
Y = ± 5
5X2 +3Y2 = 15
5X2 +3 0( )2 = 15
5X2 = 15
X2 = 5
X = ± 5
Y
X
Y
X2 + 5Y2 = 20
0( )2 + 5Y2 = 20
5Y2 = 20
Y2 = 4
Y = ±2
Points� 0,2( )�and� 0,−2( )X2 + 5Y2 = 20
X2 + 5 0( )2 = 20
X2 = 20
X
15. X Y
Y
Y
YY
2 2
2 2
2
2
5 20
0 5 20
5 20
42
0 2
+ =
( ) + =
=== ±
Points ,(( ) −( )+ =
+ ( ) =
== ± ±
,and
X Y
X
X
X
0 2
5 20
5 0 20
20
20 4
2 2
2 2
2
≈ ..
. ,
5
4 5 0Points 4.5,0
graph
( ) −( )and
see
3
12
2Y = 12
Y2 = 6
Y = ± 6
Y
X
3X2 + 2Y2 = 12
3X2 + 2 0( )2 = 12
3X2 = 12
X2 = 4
X = ± 4
5X2 +3Y2 = 15
5 0( )2 +3Y2 = 15
3Y2 = 15
Y2 = 5
Y = ± 5
5X2 +3Y2 = 15
5X2 +3 0( )2 = 15
5X2 = 15
X2 = 5
X = ± 5
Y
X
X2 + 5Y2 = 20
0( )2 + 5Y2 = 20
5Y2 = 20
Y2 = 4
Y = ±2
Points� 0,2( )�and� 0,−2( )X2 + 5Y2 = 20
X2 + 5 0( )2 = 20
X2 = 20
X = ± 20 ≈ ±4.5
Points� 4.5,0( ) ( )
aLGeBra 1
sYsteMatic reVieW 34c - sYsteMatic reVieW 34c
soLutions302
16. X Y
Y
Y
+( ) + −( ) =
−( ) +( ) + −( ) =
−( ) =
4 4 16
4 4 4 16
4 16
2 2
2 2
2
YY
Y
Y
Y
Y
and
− = ±− ==− = −=
−( ) −
4 4
4 4
8
4 4
0
4 8 4Points , , 00
4 4 16
4 4 4 16
4 16
2 2
2 2
2
( )+( ) + −( ) =
+( ) + ( ) −( ) =
+( ) =
X Y
X
X
XX
X
X
X
X
and
+ = ±+ ==+ = −= −
( ) −
4 4
4 4
0
4 4
8
0 4 8Points , , 44( )see graph
16. X Y
Y
Y
+( ) + −( ) =
−( ) +( ) + −( ) =
−( ) =
4 4 16
4 4 4 16
4 16
2 2
2 2
2
YY
Y
Y
Y
Y
and
− = ±− ==− = −=
−( ) −
4 4
4 4
8
4 4
0
4 8 4Points , , 00
4 4 16
4 4 4 16
4 16
2 2
2 2
2
( )+( ) + −( ) =
+( ) + ( ) −( ) =
+( ) =
X Y
X
X
XX
X
X
X
X
and
+ = ±+ ==+ = −= −
( ) −
4 4
4 4
0
4 4
8
0 4 8Points , , 44( )see graph
15
X2 = 5
X = ± 5
Y
X
Y
X
X2 + 5Y2 = 20
0( )2 + 5Y2 = 20
5Y2 = 20
Y2 = 4
Y = ±2
Points� 0,2( )�and� 0,−2( )X2 + 5Y2 = 20
X2 + 5 0( )2 = 20
X2 = 20
X = ± 20 ≈ ±4.5
Points� 4.5,0( )�and� −4.5,0( )see graph
X + 4( )2 + Y − 4( )2 = 16
−4( ) + 4( )2 + Y − 4( )2 = 16
Y − 4( )2 = 16
Y − 4 = ±4
Y − 4 = 4
Y = 8
Y − 4 = −4
Y = 0
Points −4,�8( )�and� −4,�0( )
X + 4( )2 + Y − 4( )2 = 16
X + 4( )2 + 4( ) − 4( )2 = 16
X + 4( )2 = 16
X + 4 = ±4
X + 4 = 4
X = 0
X + 4 = −4
X
Systematic Review 34CSystematicReview 33C1. X Y
Y
YY
2 2
2 2
2
9
0 9
93
+ =
( ) + =
== ±
2.
3.
4.
X Y
X
XX
2 2
2 2
2
9
0 9
93
0 0
9 3
+ =
+ ( ) =
== ±
( )=
,
Y
X
Y
X
X2 + Y2 = 9
X2 + 0( )2 = 9
X2 = 9
X = ±3
0,0( )
X − 1( )2 + Y − 2( )2 = 9
X − 1( )2 + 2( ) − 2( )2 = 9
X
5. X Y
Y
YY
−( ) + −( ) =
( ) −( ) + −( ) =
−( ) =− = ±
1 2 9
1 1 2 9
2 92
2 2
2 2
2
33
Y
Y
− ==
2 3
5
Y
Y
− = −= −
2 3
1
6. X Y
X
XX
−( ) + −( ) =
−( ) + ( ) −( ) =
−( ) =− = ±
1 2 9
1 2 2 9
1 91
2 2
2 2
2
33
X
X
− ==
1 3
4
X
X
− = −= −
−
1 3
2
4 2,
X
X
− = −= −
−
1 3
2
4 2,
7.
8.
1 2
9 3
,( )=
Y
X
Y
X
X2 + Y2 = 9
X2 + 0( )2 = 9
X2 = 9
X = ±3
0,0( )
aLGeBra 1
sYsteMatic reVieW 34c - sYsteMatic reVieW 34c
soLutions 303
9. 4 9 36
4 0 9 36
9 36
42
2 2
2 2
2
2
X Y
Y
Y
YY
+ =
( ) + =
=== ±
1
3125� 4090
2125
965
1
625�965
625
340
2
125�340
250
90
Y
X
9
X − 1( ) + 2( ) − 2( ) = 9
X − 1( )2 = 9
X − 1= ±3
X − 1= 3
X = 4
X − 1= −3
X = −2
4,−2
1,2( )
4X2 + 9Y2 = 36
4X2 + 9 0( )2 = 36
4X2 = 36
X2 = 9
X = ±3
83 is the largest power of 8 ≤ 1,721
83 = 512;�82 = 64;�81 = 8;�80 = 1
3
512�1721
1536
185
2
64�185
128
57
7
8�57
56
1
1
1�1
1
0
3 × 83 + 2 × 82 + 7 × 81 + 1× 80 = 32718
55 is the largest power of 5 ≤ 3,125
55 = 3125;�54 = 625;�53 = 125;�52 =
25;�51 = 5;�50 = 1
3
25�90
75
15
3
5�15
15
0
0
1�0
0
0
1 5 4 3 2 1 0
10. 4 2 9 2 36
4 2 9 02
36
4 2 36
2 9
3
X Y
X
X
X
X
+ =
+ ( ) =
=
== ±
11. 83
5
is the largest power
of 8 ≤ 1,721
83 = 112 82 64 81 8 80 1
3
512 17211536
185
2
64 1
; ; ;= = =
885128
57
7
8 5756
1
1
1 11
0
3 83 2 82 7 81 1 80 3× + × + × + × = 22718
12. 5
3125
5 is the largest power
of 5 ≤ 3,125
55 = ; ; ;
; ;
5 625 5 125
5 25 5 5 5 1
1
3125 409031
4 3
2 1 0
= =
= = =
225
965
1
625 965625
340
2
125 340250
90
3
25 9075
15
3
5 15515
0
0
1 00
0
1 5 1 5 2 5 3 5
3 5 0 5 112330
5 4 3 2
1 0
× + × + × + × +
× + × = 55
13. 654 6 7 5 7 4 7
6 49 5 7 4 1
294 35 4
72 1 0= × + × + × =
( ) + ( ) + ( ) =+ + ==
= × + × + × =( ) + ( ) +
333
8 0 8 12 11 12 0 12
8 144 111212
2 1 014. B
00 1
1 152 132 0 1 284
1 000 500 70 000
1 10
( ) =+ + =× × =
×
, ,
, ,15.33 2 4
3 2 4
9
5 10 7 10
1 5 7 10 10 10
35 10
( ) ×( ) ×( ) =× ×( ) × ×( ) =× = 33 5 10 4 10 1
000058 0023
5 8 10
10 10.
. .
.
× × ( )× =
× −
≈ SD
16.55 3
5 3
8
2 3 10
5 8 2 3 10 10
13 34 10
( ) ×( ) =×( ) ×( ) =× =
−
− −
−
.
. .
.
11 334 10 1 3 10 27 7. .× × ( )− −≈ SD
17. Y X
Y X X XX
X
X
= +
+ = − => +( ) + = −+ = −
= −
= −
2 2
4 4 2 2 4 46 2 4
6 666
XX
Y X YYY
= −
= + => = −( ) += − +=
−( )
1
2 2 2 1 22 2
0
1 0,
aLGeBra 1
sYsteMatic reVieW 34c - sYsteMatic reVieW 34D
soLutions304
18. 3 2 1 3 2 1
23
1 3 3 2
Y X Y X
Y X Y X
− = − => = −
= +
−( ) => − = − −−
= −= −
3
0 0 40 4
When a result like thiis is obtained,
it means that there is no solutiion
for this set of problems. Another
way of arrriving at this conclusion
is to put both of thhe equations
into the Y-intercept form, and takke
note of the fact that they have the
same sloope but different intercepts.
Since parallel liines never cross,
there is no solution.
19. 2 162 2 81
2 9 9
2
5 4
2 2
Y Y Y Y
Y Y Y
Y Y
− = ( ) −( ) =( ) −( ) +( ) =( ) −33 3 9
1 1 1
1 1
2
8 4 4
2 2
( ) +( ) +( )− = −( ) +( ) =−( ) +(
Y Y
Y Y Y
Y Y
20.
)) +( ) =−( ) +( ) +( ) +( )
Y
Y Y Y Y
4
2 4
1
1 1 1 1
Systematic Review 34DSystematicReview 33D1. 2 2 8
2 0 2 8
2
2 2
2 2
2
X Y
Y
Y
+ =
( ) + =
= 88
42
2YY== ±
2.
3.
2 2 8
2 2 0 8
2 8
42
0 0
2 2
2 2
2
2
X Y
X
X
XX
+ =
+ ( ) =
=== ±
( ),
Y
X
Y
X
2X2 + 2Y2 = 8
2 0( )2 + 2Y2 = 8
2Y2 = 8
Y2 = 4
Y = ±2
2X2 + 2Y2 = 8
2X2 + 2 0( )2 = 8
2X2 = 8
X2 = 4
X = ±2
0,0( )
2X2 + 2Y2 = 8
X2 + Y2 = 4� dividing both sides by 2( )r = 4 = 2
X +1( )2 + Y +3( )2 = 4
−1( ) +1( )2 + Y +3( )2 = 4
Y +3( )2 = 4
Y +3 = ±2
Y +3 = 2
Y = −1
Y +3 = −2
Y = −5
−1,−5
X +1( )2 + Y +3( )2 = 4
X2
4. Note that this can be simplified:
2X2 + =2 2Y 88
2 2 4
4 2
X Y
r
+ =
= =
(dividing both sides by 2)
5. X Y
Y
Y
+( ) + +( ) =
−( ) +( ) + +( ) =
+( ) =
12
32
4
1 12
32
4
32
4
YY + = ±3 2
Y
Y
+ == −
3 2
1
Y
Y
+ = −= −
− −
3 2
5
1 5,
Y
Y
+ = −= −
− −
3 2
5
1 5,
Y
X
Y
X
2X2 + 2Y2 = 8
2 0( )2 + 2Y2 = 8
2Y2 = 8
Y2 = 4
Y = ±2
2X2 + 2Y2 = 8
2X2 + 2 0( )2 = 8
2X2 = 8
X2 = 4
X = ±2
0,0( )
2X2 + 2Y2 = 8
X2 + Y2 = 4� dividing both sides by 2( )r = 4 = 2
X +1( )2 + Y +3( )2 = 4
−1( ) +1( )2 + Y +3( )2 = 4
Y +3( )2 = 4
Y +3 = ±2
Y +3 = 2
Y = −1
Y +3 = −2
Y = −5
−1,−5
X +1( )2 + Y +3( )2 = 4
X +1( )2 + −3( ) +3( )2 = 4
X +1( )2 = 4
X +1= ±2
6. X Y
X
X
+( ) + +( ) =
+( ) + −( ) +( ) =
+( ) =
12
32
4
12
3 32
4
12
4
XX + = ±1 2
X
X
+ ==
1 2
1
X
X
+ = −= −
−
1 2
3
1 3,
X
X
+ = −= −
−
1 2
3
1 3,
aLGeBra 1
sYsteMatic reVieW 34D - sYsteMatic reVieW 34D
soLutions 305
7.
8.
9.
− −( )=
+ =
( ) + =
==
1 3
4 2
9 4 36
9 0 4 36
4 36
2 2
2 2
2
2
,
X Y
Y
Y
Y 993Y = ±
10. 9 4 36
9 4 0 36
9 36
42
2 2
2 2
2
2
X Y
X
X
XX
+ =
+ ( ) =
=== ±
2
Y +3 = 2
Y = −1
Y +3 = −2
Y = −5
−1,−5
Y
X
X +1( )2 + Y +3( )2 = 4
X +1( )2 + −3( ) +3( )2 = 4
X +1( )2 = 4
X +1= ±2
X +1= 2
X = 1
X +1= −2
X = −3
1,−3
−1,−3( )
4 = 2
9X2 + 4Y2 = 36
9 0( )2 + 4Y2 = 36
4Y2 = 36
Y2 = 9
Y = ±3
9X2 + 4Y2 = 36
9X2 + 4 0( )2 = 36
9X2 = 36
X2 = 4
X = ±2
X2 − 2X +1
X −1� X3 −3X2 +3X −1
− X3 − X2( )2X2 +3X
− −2X2 + 2X( )X −1
− X −1( )
8X2 +12X + 29�R�59
X − 2�8X3 − 4X2 + 5X + 1
− 8X3 −16X2( )
11. X X
X X X X
X X
X X
X
2
3 2
3 2
2
2
2 1
1 3 3 1
2 3
2 2
− +
− − + −
− −( )− +
− − + XX
X
X
( )−
− −( )1
1
0
12. 8 12 29 59
2 8 4 5 1
8 16
12
2
3 2
3 2
X X R
X X X X
X X
+ +
− − + +
− −( )XX X
X X
X
X
2
2
5
12 24
29 1
29 58
59
+
− −( )+
− −( )
13. 4
256 4
4
3
is the largest power of 4 ≤ 371
44 = ; == = =
=
64 4 16 4 4
4 1
1
256 371256
115
1
64 11564
5
2 1
0
; ; ;
11
3
16 5148
3
0
4 30
3
3
1 33
0
1 4 1 4 3 4
0 4 3 4
4 3 2
1 0
× + × + × +
× + × == 113034
14. 8
8 64 8
2
2 1
is the largest power of 8 ≤ 215
= =; 88 8 1
3
64 215192
23
2
8 2316
7
7
1 77
0
3 8 2 8 7 8
0
2 1
; =
× + × + × 008327=
15. 406 4 7 0 7 6 7
4 49 0 7 6 1
196 0 6
72 1 0= × + × + × =
( ) + ( ) + ( ) =+ + = 2202
100 1 4 0 4 0 4
116 0 4 0 1
16 0
42 1 016. = × + × + × =
( ) + ( ) + ( ) =+ ++ =
×( ) ×( ) =×( ) ×( ) =×
− −
− −
0 16
3 10 2 10
3 2 10 10
6 10
5 2
5 2
17.
−−
−
−
×( ) ×( ) ×( ) =×( ) ×
7
5 2 3
5 2
4 10 5 10 2 10
4 5 2 10 10 1
18. ÷
÷ ÷ 00
10 10 1 10
3
6 5
( ) =× = ×− −
aLGeBra 1
sYsteMatic reVieW 34D - sYsteMatic reVieW 34e
soLutions306
19. Y X
Y X X X
X X
= −
= − − => −( ) = − −− = − −
3 1
4 3 19 4 3 1 3 19
12 4 3 19122 3 19 4
15 151
3 1 3 1 13 1
X X
XX
Y X YYY
+ = − += −= −
= − => = −( ) −= − −== −
− −( )+ − = −− − = − −
−
4
1 4
21 12 3 15 912 3 15 9 21
,
20. M M MM M M
66 30
5
M
M
= −=
Systematic Review 34E SystematicReview 34E1. 3 3 48
3 0 3 48
3
2 2
2 2
X Y
Y
Y
+ =
( ) + =22
2
48
164
=== ±
YY
3X2 +3Y2 = 48
3 0( )2 +3Y2 = 48
3Y2 = 48
Y2 = 16
Y = ±4
Y
X
3X2 +3Y2 = 48
3X2 +3 0( )2 = 48
3X2 = 48
X2 = 16
X = ±4
0,0( )3X2 +3Y2 = 48
X2 + Y2 = 16
r = 16 = 4
Y
2.
3.
4
3 3 48
3 3 0 48
3 48
164
0 0
2 2
2 2
2
2
X Y
X
X
XX
+ =
+ ( ) =
=== ±
( ),
.. 3 3 48
16
16 4
2 2
2 2
X Y
X Y
r
+ =+ =
= =
16
X = ±4
0,0( )3X2 +3Y2 = 48
X2 + Y2 = 16
r = 16 = 4
Y
X
Y
X
3 X +1( )2 +3 Y +3( )2 = 48
3 −1( ) +1( )2 +3 Y +3( )2 = 48
3 Y +3( )2 = 48
Y +3( )2 = 16
Y +3 = ±4
Y +3 = 4
Y = 1
Y +3 = −4
Y = −7
3 X +1( )2 +3 Y +3( )2 = 48
3 X +1( )2 +3 −3( ) +3( )2 = 48
3 X +1( )2 = 48
X +1( )2 = 16
X +1= ±4
X +1= 4
X = 3
X +1= −4
X = −5
−1,−3( )3 X +1( )2 +3 Y +3( )2 = 48
X +1( )2 + Y +3( )2 = 16
r = 16 = ±4
9X2 +16Y2 = 144
9 0( )2 +16Y2 = 144
16Y2 = 144
Y
5. 3 1 3 3 48
3 1 1 3 3 48
3 3
2 2
2 2
X Y
Y
Y
+( ) + +( ) =
−( ) +( ) + +( ) =
+( )222
48
3 16
3 4
=
+( ) =+ = ±
Y
Y
Y
Y
+ = −= −
3 4
7
Y
Y
+ ==
3 4
1
6. 3 1 3 3 48
3 1 3 3 3 48
3 1
2 2
2 2
X Y
X
X
+( ) + +( ) =
+( ) + −( ) +( ) =
+( )222
48
1 161 4
=
+( ) =+ = ±
XX
X
X
+ ==
1 4
3
X
X
+ = −= −
1 4
5
7.
8.
− −( )+( ) + +( ) =
+( ) + +( ) =
=
1 3
3 1 3 3 48
1 3 16
2 2
2 2
,
X Y
X Y
r 116 4
9 16 144
9 0 16 144
16 144
9
2 2
2 2
2
2
=
+ =
( ) + =
===
9. X Y
Y
Y
YY ±±3
Y
X
Y
X
3 X +1( )2 +3 Y +3( )2 = 48
3 −1( ) +1( )2 +3 Y +3( )2 = 48
3 Y +3( )2 = 48
Y +3( )2 = 16
Y +3 = ±4
Y +3 = 4
Y = 1
Y +3 = −4
Y = −7
3 X +1( )2 +3 Y +3( )2 = 48
3 X +1( )2 +3 −3( ) +3( )2 = 48
3 X +1( )2 = 48
X +1( )2 = 16
X +1= ±4
X +1= 4
X = 3
X +1= −4
X = −5
−1,−3( )3 X +1( )2 +3 Y +3( )2 = 48
X +1( )2 + Y +3( )2 = 16
r = 16 = ±4
9X2 +16Y2 = 144
9 0( )2 +16Y2 = 144
16Y2 = 144
Y2 = 9
Y = ±3
9X2 +16Y2 = 144
9X2 +16 0( )2 = 144
9X
aLGeBra 1
sYsteMatic reVieW 34e - Lesson Practice 35a
soLutions 307
7.
8.
− −( )+( ) + +( ) =
+( ) + +( ) =
=
1 3
3 1 3 3 48
1 3 16
2 2
2 2
,
X Y
X Y
r 116 4
9 16 144
9 0 16 144
16 144
9
2 2
2 2
2
2
=
+ =
( ) + =
===
9. X Y
Y
Y
YY ±±3
10. 9 16 144
9 16 0 144
9 144
164
2 2
2 2
2
2
X Y
X
X
XX
+ =
+ ( ) =
=== ±
11. X X
X X X X
X X
X X
X X
2
3 2
3 2
2
2
2 1
1 3 3 1
2 3
2 2
+ +
+ + + +
− +( )+
− +
(( )+
− +( )XX
11
0
12. X X
X X X X
X X
X X
X X
2
3 2
3 2
2
2
2 3
2 4 7 6
2
2 7
2 4
+ +
+ + + +
− +( )+
− +(( )+
− +( )3 63 6
0
XX
13. 6
216
3 is the largest power
of 6 ≤ 1,054
63 = ; 66 36 6 6 6 1
4
216 1054864
190
5
36 190180
10
1
6
2 1 0= = =; ;
106
4
4
1 44
0
4 6 5 6 1 6 4 6 45143 2 1 06× + × + × × × =
14. 101111
1 2 0 2 1 2 1 2 1 2 1 2
1 32
25 4 3 2 1 0
=
× + × + × + × + × + × =( ) + 00 16 1 8 1 4 1 2 11
32 0 8 4 2 1 47
( ) + ( ) + ( ) + ( ) + ( ) =+ + + + + =
15. 50 60 55 55
3 000 3 025
× < ×<, ,
16. 41
43 5601
174 240
174 240
22acres
acre× =, ft , ft
, ftt , ft
.
.
2 2
4 3
4
200 000
4 2 10 6 10
4 2 6 10
<
×( ) ×( ) =( )
−17. ÷
÷ ÷÷10 7 10 7 103 7 6−( ) = × = ×.
18. 7 10 8 10 4 10 1 4 10
7 8
8 0 3 5×( ) ×( ) ×( ) ×( ) =
×(÷ .
)) ×( ) ×( ) ×( ) =
( )÷ ÷
÷
4 1 4 10 10 10 10
56 5 6 1
8 0 3 5.
. 00 10 10 10 1 10 108 8 0 1÷( ) = × = × or
19.
20.
X X X
X X X
4 2 2
2
16 4 4
2 2 4
1 25
− = −( ) +( ) =−( ) +( ) +( )
+. .88 1 3125 80 100 30
80 30 125 10080 5
116
AA
AA
A
− =+ − =
= − +=
=
.
Lesson Practice 35A
1. X Y
0 0
1 1
1 1
2 4
2 4
−
−
Y
X
Y
X
X Y
0 0
1 1
−1 1
2 4
−2 4
X Y
2 3
−2 −3
3 2
−3 −2
1 6
−1 −6
6 1
−6 −1
X Y
0 0
1 2
2 8
3 18
Y
X
aLGeBra 1
Lesson Practice 35a - Lesson Practice 35B
soLutions308
2. X Y
2 3
2 3
3 2
3 2
1 6
1 6
6 1
6 1
− −
− −
− −
− −
Y
X
Y
X
X Y
0 0
1 1
−1 1
2 4
−2 4
X Y
2 3
−2 −3
3 2
−3 −2
1 6
−1 −6
6 1
−6 −1
X Y
0 0
1 2
2 8
3 18
−1 2
−2 8
Y
X
X Y
1 −2
−1 2
2 −1
−2 1
12
−4
− 12
4
4 − 12
−4 12
X Y
0 −3
1 −2
−1 −2
2 1
−2 1
Y
X
X Y
2 4
−2 −4
4 2
−4 −2
113
6
−113
−6
6 113
113
Y
X
Y
X
3. X Y0 01 22 83 181 22 8
−−
Y
X
Y
X
−1 1
2 4
−2 4
X Y
2 3
−2 −3
3 2
−3 −2
1 6
−1 −6
6 1
−6 −1
X Y
0 0
1 2
2 8
3 18
−1 2
−2 8
Y
X
X Y
1 −2
−1 2
2 −1
−2 1
12
−4
− 12
4
4 − 12
−4 12
X Y
0 −3
1 −2
−1 −2
2 1
−2 1
Y
X
X Y
2 4
−2 −4
4 2
−4 −2
113
6
−113
−6
6 113
−6 −113
Y
X
Y
X
4. X Y
1 2
1 2
2 1
2 1
12
4
12
4
4 12
4 12
−−
−−
−
−
−
−
Y
X
Y
X
X Y
0 0
1 1
−1 1
2 4
−2 4
X Y
2 3
−2 −3
3 2
−3 −2
1 6
−1 −6
6 1
−6 −1
X Y
0 0
1 2
2 8
3 18
−1 2
−2 8
Y
X
X Y
1 −2
−1 2
2 −1
−2 1
12
−4
− 12
4
4 − 12
−4 12
X Y
0 −3
1 −2
−1 −2
2 1
−2 1
Y
X
X Y
2 4
−2 −4
4 2
−4 −2
113
6
−113
−6
6 113
Y
X
Y
X
5. X Y
0 3
1 2
1 2
2 1
2 1
−−
− −
−
Y
X
Y
X
X Y
0 0
1 1
−1 1
2 4
−2 4
X Y
2 3
−2 −3
3 2
−3 −2
1 6
−1 −6
6 1
−6 −1
X Y
0 0
1 2
2 8
3 18
−1 2
−2 8
Y
X
X Y
1 −2
−1 2
2 −1
−2 1
12
−4
− 12
4
4 − 12
−4 12
X Y
0 −3
1 −2
−1 −2
2 1
−2 1
Y
X
X Y
2 4
−2 −4
4 2
−4 −2
113
6
−113
−6
6 113
Y
X
Y
X
6. X Y2 42 44 24 2
1 13
6
1 13
6
6 1 13
6 1 13
− −
− −
− −
− −
−4 12
X Y
0 −3
1 −2
−1 −2
2 1
−2 1
X Y
2 4
−2 −4
4 2
−4 −2
113
6
−113
−6
6 113
−6 −113
Y
X
Y
X
Lesson Practice 35B1. X Y
0 0
1 12
2 2
3 92
1 12
2 2
−
−
Lesson Practice 34B 1.
2.
3.
4.
Y
X
X Y
0 0
1 12
2 2
3 92
−1 12
−2 −2
X Y
−1 3
1 −3
−3 1
3 −1
112
−2
−112
2
−2 112
2 −112
X Y
0 1
1 2
2 5
−1 2
−2 5
X Y
1 −4
−1 4
4
Y
X
Y
X
2. X Y−
−−
−
−
−
−
−
1 31 33 13 1
1 12
2
1 12
2
2 1 12
2 1 12
Lesson Practice 34B 1.
2.
3.
4.
Y
X
X Y
0 0
1 12
2 2
3 92
−1 12
−2 −2
X Y
−1 3
1 −3
−3 1
3 −1
112
−2
−112
2
−2 112
2 −112
X Y
0 1
1 2
2 5
−1 2
−2 5
X Y
1 −4
−1 4
4 −1
Y
X
Y
X
Y
X
aLGeBra 1
Lesson Practice 35B - sYsteMatic reVieW 35c
soLutions 309
3. X Y0 11 22 51 22 5
−−
3.
4.
5.
6.
1
112
−112
2
−2 112
2 −112
X Y
0 1
1 2
2 5
−1 2
−2 5
X Y
1 −4
−1 4
4 −1
−4 1
113
−3
−113
3
6 − 23
−6 23
X Y
0 0
1 −1
2 −4
−1 −1
−2 −4
X Y
1 5
−1 −5
5 1
−5 −1
114
4
−114
−4
0 *
*no�possible�value
Y
X
Y
X
Y
X
Y
X
4. X Y1 41 44 14 1
1 13
3
1 13
3
6 23
6 23
−−
−−
−
−
−
−
3.
4.
5.
6.
−112
2
−2 112
2 −112
X Y
0 1
1 2
2 5
−1 2
−2 5
X Y
1 −4
−1 4
4 −1
−4 1
113
−3
−113
3
6 − 23
−6 23
X Y
0 0
1 −1
2 −4
−1 −1
−2 −4
X Y
1 5
−1 −5
5 1
−5 −1
114
4
−114
−4
0 *
*no�possible�value
Y
X
Y
X
Y
X
Y
X
5. X Y0 01 12 41 12 4
−−
− −− −
3.
4.
5.
6.
2 112
2 −112
X Y
0 1
1 2
2 5
−1 2
−2 5
X Y
1 −4
−1 4
4 −1
−4 1
113
−3
−113
3
6 − 23
−6 23
X Y
0 0
1 −1
2 −4
−1 −1
−2 −4
X Y
1 5
−1 −5
5 1
−5 −1
114
4
−114
−4
0 *
*no�possible�value
Y
X
Y
X
Y
X
Y
X
6. X Y
no possible value
1 51 55 15 1
1 14
4
1 14
4
0
− −
− −
− −
*
*
3.
4.
5.
6.
−2 112
2 −112
X Y
0 1
1 2
2 5
−1 2
−2 5
X Y
1 −4
−1 4
4 −1
−4 1
113
−3
−113
3
6 − 23
−6 23
X Y
0 0
1 −1
2 −4
−1 −1
−2 −4
X Y
1 5
−1 −5
5 1
−5 −1
114
4
−114
−4
0 *
*no�possible�value
Y
X
Y
X
Y
X
Y
X
Systematic Review 35C
1. X Y0 01 11 12 42 4
−
−
Y
X
Y
X
53 is the largest power of 5 less than 131
53 = 125;�52 = 25;�51 = 5;�50 = 1
1
125�131
125
6
0
25�6
0
6
1
5�6
5
1
1
1�1
1
0
1× 53 + 0 × 52 + 1× 51 + 1× 50 = 10115
11112 = 1× 23 + 1× 22 + 1× 21 + 1× 20 =
1 8( ) + 1 4( ) + 1 2( ) + 11( ) = 8 + 4 + 2 + 1= 15
2023 = 2 × 32 + 0 × 31 + 2 × 30 =
2 9( ) + 0 3( ) + 2 1( ) = 18 + 0 + 2 = 20
15 < 20
2 ft2
1× 12�in
1ft× 12�in
1ft= 288�in
288
5,616
179312 =
1× 123 + 7 × 122 + 9 × 121 + 3 × 120 =11,728( ) + 7 144( ) + 9 12( ) + 3 1( ) =1,728 + 1,008 + 108 + 3 = 2,847
2. X Y1 11 1
3 13
3 13
5 15
5 15
− −
− −
− −
Y
X
Y
X
53 is the largest power of 5 less than 131
53 = 125;�52 = 25;�51 = 5;�50 = 1
1
125�131
125
6
0
25�6
0
6
1
5�6
5
1
1
1�1
1
0
1× 53 + 0 × 52 + 1× 51 + 1× 50 = 10115
11112 = 1× 23 + 1× 22 + 1× 21 + 1× 20 =
1 8( ) + 1 4( ) + 1 2( ) + 11( ) = 8 + 4 + 2 + 1= 15
2023 = 2 × 32 + 0 × 31 + 2 × 30 =
2 9( ) + 0 3( ) + 2 1( ) = 18 + 0 + 2 = 20
15 < 20
5,616
179312 =
1× 123 + 7 × 122 + 9 × 121 + 3 × 120 =11,728( ) + 7 144( ) + 9 12( ) + 3 1( ) =1,728 + 1,008 + 108 + 3 = 2,847
3.
4.
5.
6.
7.
8.
line
circle
ellipse
line
hyperbola
paraboola
9. 1793 1 12 7 12 9 12 3 12
11 728 7 14412
3 2 1 0= × + × + × + × =
( ) + (, )) + ( ) + ( ) =+ + + =
9 12 3 1
1 728 1 008 108 3 2 847, , ,
10. 53 is the largest power of
5 less than 1331
53 = = = =125 52 25 51 5 50 1
1
125 131
125
6
0
25
; ; ;
6
0
6
1
5 6
5
1
1
1 1
1
0
1 53 0 52 1 51 1 50 10115× + × + × + × =
aLGeBra 1
sYsteMatic reVieW 35c - sYsteMatic reVieW 35D
soLutions310
11. 1111 1 2 1 2 1 2 1 2
1 8 1 4 1 2 112
3 2 1 0= × + × + × + × =
( ) + ( ) + ( ) + ( )) = + + + =
= × + × + × =
( ) + ( ) + ( )
8 4 2 1 15
202 2 3 0 3 2 3
2 9 0 3 2 13
2 1 0
== + + =<
18 0 2 20
15 20
12. 21
121
121
288
288 289
2ft
ft ft× × =
<
in in in
13. 7 10 1 4 10
7 1 4 10 10 5 10
8 6
8 6 14
×( ) ×( ) =( )( ) = ×
−
− −
÷
÷ ÷
.
.
14.
. . .2 4 10 2 6 10 6 10 5 2 104 5 5 7×( ) ×( ) ×( ) ×( )− − −÷ =
×( ) ×( ) ×( ) ×− − −. . .2 4 2 6 6 5 2 10 10 10 104 5 5 7÷ ÷ (( ) =
( )( ) =× = ×
−6 24 31 2 10 10
2 10 2 10
1 12
13 12
. .
.
÷ ÷
15. 23
45
1730
X
multiply
+ = −
each term by 30,
to elimminate fractions:
301
⋅ + ⋅ = ⋅ −
+
23
301
45
301
1730
20 2
X
X 44 17
20 17 24
20 41
4120
2 120
= −= − −= −
= − = −
X
X
X
16. 56
13
47
0
421
− + =
⋅
X
multiply each term by 42:
556
421
13
421
47
42 0
35 14 24 0
35 24 1
+ ⋅ − + ⋅ = ( )− + =
+ =
X
X
44
59 14
5914
4 314
X
X
X
=
= =
17.
18.
19.
20.
78 72 5,616
Y3 Y Y Y2 1
Y Y 1 Y 1
on graph
m 4 11 1
52
Y mX b
1 52
1 b
1 52
b
22
52
b; b 32
Y 52
X 32
or 2Y 5X 3
( )( ) ( )
( )( ) ( ) ( )
( )( )
( ) ( )
=
− = − =− +
= − −− −
= −
= +
= − − +
= +
− = = −
= − − + = −
17.
18.
19.
20.
78 72 5,616
Y3 Y Y Y2 1
Y Y 1 Y 1
on graph
m 4 11 1
52
Y mX b
1 52
1 b
1 52
b
22
52
b; b 32
Y 52
X 32
or 2Y 5X 3
( )( ) ( )
( )( ) ( ) ( )
( )( )
( ) ( )
=
− = − =− +
= − −− −
= −
= +
= − − +
= +
− = = −
= − − + = −
Y
X
41
X = −4120
= −2 120
56
− 13
X + 47
= 0
multiply each term by 42:
421
⋅ 56
+ 421
⋅ − 13
X + 421
⋅ 47
= 42 0( )
35 − 14X + 24 = 0
35 + 24 = 14X
59 = 14X
5914
= X = 4 314
78( ) 72( ) = 5,616
Systematic Review 35D
1. X Y
0 0
1 2
1 2
2 8
2 8
−
−
X Y
0 0
1 2
−1 2
2 8
−2 8
X Y
.5 12
−.5 −12
1 6
−1 −6
2 3
−2 −3
3 2
−3 −2
Y
X
Y
X
1324 = 1× 42 + 3 × 41 + 2× 40 =( ) ( ) ( )
2. X Y
.
.
5 12
5 12
1 6
1 6
2 3
2 3
3 2
3 2
− −
− −
− −
− −
X Y
0 0
1 2
−1 2
2 8
−2 8
X Y
.5 12
−.5 −12
1 6
−1 −6
2 3
−2 −3
3 2
−3 −2
Y
X
Y
X
132 = 1× 42 + 3 × 41 + 2× 40 =
aLGeBra 1
sYsteMatic reVieW 35D - sYsteMatic reVieW 35D
soLutions 311
3.
4.
5.
6.
7.
parabola
circle
hyperbola
parabola
elllipse
line8.
9. 1324 1 42 3 41 2 40
1 16 3 4 2 1 16 12
= × + × + × =
( ) + ( ) + ( ) = + ++ =2 30
10. 83
512
is the largest power
of 8 < 2,348
83 = ; 882 64 81 8 80 1
4
512 23482048
300
4
64 300256
44
5
= = =; ;
88 4440
4
4
1 44
0
4 83 4 82 5 81 4 80 44548× + × + × + × =
11. 17 3 2 5 4
14 2 5 5 4
14 2 25 4
28
2− ⋅ −( ) > − −⋅ − > − ×( ) −⋅ − > − −
− > −−
⋅ <<
×( ) ×( )−
29
47 43 45
2 021 2 025
6 10 2 5 10
2
7 9
12.
13.
, ,
. == ×( ) ×( ) =× = ×
×
−
− −
−
6 2 5 10 10
15 10 1 5 10
2 10
7 9
2 1
1
.
.
Or iff the student took
significant digits into accoount.
Either answer is acceptable.
11. 17 3 2 5 4
14 2 5 5 4
14 2 25 4
28
2− ⋅ −( ) > − −⋅ − > − ×( ) −⋅ − > − −
− > −−
⋅ <<
×( ) ×( )−
29
47 43 45
2 021 2 025
6 10 2 5 10
2
7 9
12.
13.
, ,
. == ×( ) ×( ) =× = ×
×
−
− −
−
6 2 5 10 10
15 10 1 5 10
2 10
7 9
2 1
1
.
.
Or iff the student took
significant digits into accoount.
Either answer is acceptable.
14.
. .1 1 10 1 5 10 5 10 3 109 8 1 6×( ) ×( ) ×( ) ×( ) − −÷ ==
×( ) ×( ) ×( ) ×( ) − −. .1 1 1 5 5 3 10 10 10 109 8 1 6÷ ÷ ==
( )( ) =× = ×
×
− −1 65 15 10 10
11 10 1 1 10
1 10
1 5
4 3
3
.
. .
÷ ÷
Or iif the student took
significant digits into acccount.
Either answer is acceptable.
15. Y Y− − =2 6÷ YY Y
mi
mi
C
− − −( ) =
× =
2 6 4
6
251
5 2801
1 32016.
17.
. , ft , ft
DD C
D D CC D C D D C
C D C D
3 2
9 2 86 3 2 9 2 8
6 2 8 3 9 2 0
− −−
+ + −( ) + +
= =
= 114 14= D
18. 3 4
3 4
3
2 24 0 2
1
2
2
4 0 2
1
2
2
X Y Y Y Y
X
Y
X
Y
X
Y
X
− −
−
+ + −( )−
+ =
+ =
++
+ ⋅
41
4
1 2
2
2
2
X Y
find
X
X
X
X
common denominators:
3Y2 YY
X
X Y
X
Y X Y
X
X Y XY is
2
2
3 2
2
2 3 2
2
2 2 2
1
4
3 4
3 4
=
+ =
+
+−
3Y
al
2
sso acceptable
see graph
see graph m 14
19.
20. =
18. 3 4
3 4
3
2 24 0 2
1
2
2
4 0 2
1
2
2
X Y Y Y Y
X
Y
X
Y
X
Y
X
− −
−
+ + −( )−
+ =
+ =
++
+ ⋅
41
4
1 2
2
2
2
X Y
find
X
X
X
X
common denominators:
3Y2 YY
X
X Y
X
Y X Y
X
X Y XY is
2
2
3 2
2
2 3 2
2
2 2 2
1
4
3 4
3 4
=
+ =
+
+−
3Y
al
2
sso acceptable
see graph
see graph m 14
19.
20. =
2,025
Or�2×10−1�if the student took significant
digits into account. Either answer is
acceptable.
1.1× 10−9( ) 1.5 × 108( )�� �� ÷ 5 × 101( ) 3 × 10−6( )�� �� =
1.1× 1.5( ) ÷ 5×3( )( ) 10−9 × 108( )÷ 101 × 10−6( )( ) =1.65 ÷ 15( ) 10−1 ÷ 10−5( ) =
.11× 104 = 1.1× 103
Or�1× 103�if the student took significant
digits into account. Either answer is
acceptable.
Y−2 ÷ Y−6 = Y−2− −6( ) = Y4
.25mi1
× 5,280�ft
1mi= 1,320�ft
C6D3C2
D−9D−2C8= C6D3C2D9D2C−8 =
C6+2+ −8( )D3+9+2 = C0D14 = D14
3X−2Y2 + 4Y4Y0Y−2
X−1= 3Y2
X2+ 4Y4+0+ −2( )
X−1=
3Y2
X2+ 4X1Y2
1�find common
denominators:
3Y2
X2+ X2
X2⋅ 4XY2
1=
3Y2
X2+ 4X3Y2
X2=
3Y2 + 4X3Y2
X2
3X−2Y2 + 4XY2�is also acceptable
Y
X
#19
#20
aLGeBra 1
sYsteMatic reVieW 35e - sYsteMatic reVieW 35e
soLutions312
Systematic Review 35E
1. X Y0 01 31 32 122 12
−
−
X Y
0 0
1 3
−1 3
2 12
−2 12
X Y
1 −10
−1 10
2 −5
−2 5
5 −2
−5 2
1517 = 1×72 +5×71+1×70 =
1 49( ) +5 7( ) +11( ) =49 +35+1= 85
44 is the largest power of 4 ≤ 291
44 = 256;�43 = 64;�42 = 16;�41= 4;�40 = 1
1
256�291
256
35
0
64�35
0
35
2
16�35
32
3
0
4�3
0
3
3
1�3
3
0
1× 44 + 0 × 43 + 2× 42 + 0 × 41+3× 40 = 102034
Y
X
Y
X
3 ⋅2 ⋅ −2( ) 24 ÷ −3
−12 − 8
12 > −8
32( )13 287( )2
93 2< 82,369
93,000,000 = 9.3×107
.038 = 3.8 ×10−2
900 g .035�oz
1g
2. X Y1 101 102 52 55 25 2
−−
−−
−−
X Y
0 0
1 3
−1 3
2 12
−2 12
X Y
1 −10
−1 10
2 −5
−2 5
5 −2
−5 2
1517 = 1×72 +5×71+1×70 =
1 49( ) +5 7( ) +11( ) =49 +35+1= 85
44 is the largest power of 4 ≤ 291
44 = 256;�43 = 64;�42 = 16;�41= 4;�40 = 1
1
256�291
256
35
0
64�35
0
35
2
16�35
32
3
0
4�3
0
3
3
1�3
3
0
1× 44 + 0 × 43 + 2× 42 + 0 × 41+3× 40 = 102034
Y
X
Y
X
3 ⋅2 ⋅ −2( ) 24 ÷ −3
−12 − 8
12 > −8
32( )13 287( )2
93 2< 82,369
93,000,000 = 9.3×107
.038 = 3.8 ×10−2
900 g× .035�oz
1g= 31.5�oz
3.
4.
5.
6.
7.
8.
ellipse
hyperbola
line
circle
line
circlee
9. 151 1 7 5 7 1 7
1 49 5 7 11
49 35 1 8
72 1 0= × + × + × =
( ) + ( ) + ( ) =+ + = 55
10. 4
256 4
4
3
is the largest power
of 4 ≤ 291
44 = ; == =
= =
64 4 16
4 4 4 1
1
256 291256
35
0
64 350
35
2
1
2
1 0
; ;
;
66 3532
3
0
4 30
3
3
1 33
0
1 4 0 4 2 4 0 4 3 4 104 3 2 1 0× + × + × + × + × = 22034
11. 3 2 2 24 3
12 8
12 8
⋅ ⋅ −( ) > −− > −
> −
÷
12. 3 287
9 82 369
213 2
3
( ) < ( )( ) < ,
13.
14.
15.
93 000 000 9 3 10
038 3 8 10
900
1
7
2
, , .
. .
.
= ×
= ×
×
−
g 00351
31 5
1
1361
361
1 22
.
,
ozg
oz
yd inyd
inyd
=
× × =16. 996
25 25
5 5
243
2
3 2
in
A A A A
A A A
17.
18.
− = ( ) −( ) =( ) −( ) +( )
−− = ( ) −( ) =( ) −( ) +( ) =( ) −( ) +( )
3 3 81
3 9 9
3 3 3 9
4 4
2 2
X X
X X
X X ++( )X2
19. X X X X
X
X
X
+ +( ) + − − =+ − =
==
4 5 1 2 2
4 5 1 2
8 2
4
20. 5 5 4 45
5 20 45
5 25
5
D
D
D
D
+ ( )( ) =+ =
==
Honors Lesson 1H - Honors Lesson 2H 313aLGeBra 1
Honors Lesson 1H1. 1 1
232
23
32
66
1
34
32
1 18
=
× = =
× =
cup shortening
cup off sugar
eggs rounds to
table
1 32
1 12
2
1 32
1 12
× = ( )
× = sspoons of milk
teaspoons vanilla1 32
1 12
74
32
2
× =
× = 118
2 58
12
32
34
=
× =
teaspoons
of baking powder
teaspooon of salt
cups of rolled oats34
32
98
1 18
14
32
× = =
× == 38
cup of dried fruit
original recipe made th2. rree dozen
or cookies
cookies
,
36
361
32
1082
54× = =
argfrom the l er recipe
cookies from ea54 2 27÷ = cch bowl
Total of bills
$ . $ . $ .
3. :
35 92 25 26 255 10+ + ++ ++ + =
$ .
$ . $ . $ . $ , .
$ ,
798 53
20 00 116 48 398 19 1 649 48
1 6099 00 1649 48 40 48. . $ .− = −The negative number indicattes that Daniel
is in the hole or owes that" " aamount
from
.
4. −( ) × = −−( ) + = −3 6 18
18 5 13
in
inches sstarting level
st option
nd
$
5. 1
10 20 40 80 150
2
+ + + =ooption
The ond opti
5 25 625 390 625 391 280+ + + =, $ ,
sec oon is definitely the better choice.
6. 4 3 12
3 4
× =× ==
+ = + =+ = + =
12
5 6 11 11 8 19
6 8 14 14 5 19
commutative
as
7. ;
;
ssociative
pizzas per person
pizza
8. 8 4 2
4 8 12
÷
÷
=
= per person
division is not commutative
The negative number indicattes that Daniel
is in the hole or owes that" " aamount
from
.
× = −−( ) + = −3 6 18
18 5 13
in
inches sstarting level
st option
nd
$
5. 1
10 20 40 80 150
2
+ + + =ooption
The ond opti
5 25 625 390 625 391 280+ + + =, $ ,
sec oon is definitely the better choice.
6. 4 3 12
3 4
× =× ==
+ = + =+ = + =
12
5 6 11 11 8 19
6 8 14 14 5 19
commutative
as
7. ;
;
ssociative
pizzas per person
pizza
8. 8 4 2
4 8 12
÷
÷
=
= per person
division is not commutative
Honors Lesson 2H1. There are They are. , , , , ,14 32 33 34 35 36
3
:
88 39 40 42 44 45 46 48 49
1 17
, , , , , , , , .
, ,
and
2.
$ .
$ . $ . $ .
289
1815
1 315
1 15
1 20
75 78 45 78 30 0
3.
4.
= = =
− = 00
30 00 1 5 20 00
14
712
312
712
$ . . $ .
labor
÷ =
+ = + =
/hour
5. 11012
56
56
110
560
112
56
112
10
=
× = =
− =
6. of a k usedtan
1121
12912
34
34
24 18
− = =
× =
,
gallons left
First fig7. uure out how long it would take
for him to do thhe whole job utes
is of the total tim
. min30
35
ee In equation form
T
T
T so
. :
, mi
30 35
150 3
50 50
=
== nn
min
for the whole job
of
of
15
50 10
12
50 25
=
= mmin
8.
9.
9 19 2828 4 7
7 5 12
5 4 2020 1 1919 8 27
+ ==
+ =
× =− =+ =
÷
$ . $ . $ .$ $ . $ .
yards
10. − + =+ =
20 00 35 00 15 0015 70 00 85 000
85 00 10 00 75 0075 00 22 50 52 50
$ . $ . $ .$ . $ . $ .
− =− =
Honors Solutions ν+ =ν+ = + =ν+ =+ =ν+ = + =ν+ =
5 6ν5 6+ =5 6+ =ν+ =5 6+ = 11ν11 11ν11 8 1ν8 1+ =8 1+ =ν+ =8 1+ =6 8ν6 8+ =6 8+ =ν+ =6 8+ = 14ν14 14ν14 5 1ν5 1+ =5 1+ =ν+ =5 1+ =asνas
7.ν7. ;ν;
;ν;
sociativνsociativssociativsνssociativs eνe
piνpizzasνzzas8.ν8. 8 4ν8 4 2ν2
1ν
1
8 4÷8 4ν8 4÷8 4 =ν=
Honors Solutions νHonors Solutions ν
aLGeBra 1
Honors Lesson 2H - Honors Lesson 5H
soLutions314
8.
9.
9 19 2828 4 7
7 5 12
5 4 2020 1 1919 8 27
+ ==
+ =
× =− =+ =
÷
$ . $ . $ .$ $ . $ .
yards
10. − + =+ =
20 00 35 00 15 0015 70 00 85 000
85 00 10 00 75 0075 00 22 50 52 50
$ . $ . $ .$ . $ . $ .
− =− =
Honors Lesson 3H1.
2.
3.
4.
yes
rational
rational
A bh
h
h
=
= ( )
=
12
12 12
6
12 344
2 2
30 2 10 2
30 20 210 2
5
in h
P L W
W
WW
cm W
=
= += ( ) += +==
5.
6.. d rt
t
t
t
t
=
= ( )
= ( )
=
= =
11 14
4 12
454
184
45 184518
2 12
hourrs
: u g decimals tt
p d
sin . ..
.
.
11 25 4 52 5
0 433
43
==
=7.
33 43343300 433
100
===
. dd
d ft
Honors Lesson 4H1.
2.
3.
4.
5.
6.
7.
8.
9.
2
18
1
4
9
2
4
100 75 25
Test
Test
Jo
− =hhn
David
:
:
95 90 95 93 97 470
470 5 94
98 90
+ + + + ==
+ +÷
990 75 100 453
453 5 90 6
+ + == .÷
You may have slightlyy different
results depending on how you
estimaated the scores
John had the highest average s
.
ccore
Joe sold
Jeff sold
The graphs ag
.
.
.
1.
2.
3.
4.
5.
6.
7.
8.
9.
2
18
1
4
9
2
4
100 75 25
Test
Test
Jo
− =hhn
David
:
:
95 90 95 93 97 470
470 5 94
98 90
+ + + + ==
+ +÷
990 75 100 453
453 5 90 6
+ + == .÷
You may have slightlyy different
results depending on how you
estimaated the scores
John had the highest average s
.
ccore
Joe sold
Jeff sold
The graphs ag
.
.
.
10. 25
20
rree
Jeff probably drew the first graph it
.
11. : iis unlikely
that he would have presented the datta in a way
that made it look like he had only ssold a fraction
of what Joe sold
Joe probably
.
sec .drew the ond graph
12. Answers will vary.
Honors Lesson 5H1.
2.
6
6 10 4 4
,
, ,
steps east
so steps west
( )+ −( ) = − (( )
( )( )( )
3.
4.
5.
6.
4
2
6
,
,
,
paces south
south
north
AA B C
C
C
C
northeast
2 2 2
2 2 2
2
2
4 4
32
32
32
8
+ =
+ =
=
=
( )7.
8.
,
++ =
=
=
( )
8
128
128
128
2 2
2
C
C
C
southwest,
1.
2.
6
6 10 4 4
,
, ,
steps east
so steps west
( )+ −( ) = − (( )
( )( )( )
3.
4.
5.
6.
4
2
6
,
,
,
paces south
south
north
AA B C
C
C
C
northeast
2 2 2
2 2 2
2
2
4 4
32
32
32
8
+ =
+ =
=
=
( )7.
8.
,
++ =
=
=
( )
8
128
128
128
2 2
2
C
C
C
southwest,
aLGeBra 1
Honors Lesson 6H - Honors Lesson 8H
soLutions 315
Honors Lesson 6HY
X
1.
2.
Y
X
Honors Lesson 7H1.
2.
3.
done
done
slope is negative; less steep thann 1;
Y-intercept is 1.
Line a is the best choice..
slope is positive; steeper than 1;
Y-interce
4.
ppt is 1.
Line c is the best choice.
slope is p5. oositive; less steep than 1;
Y-intercept is -1.
Liine b is the best choice.
slope is positive; 6. ssteeper than 1;
Y-intercept is 0.
Line d is the bbest choice.
slope is positive; steeper than 7. 11;
Y-intercept is 0.
Line h is the best choice.
8.. slope is positive; less steep than 1;
Y-interceept is 3.
Line f is the best choice.
slope is 9. ppositive; equal to 1;
Y-intercept is 0.
Line g iss the best choice.
slope is negative; equal
done
done
slope is negative; less steep thann 1;
Y-intercept is 1.
Line a is the best choice..
slope is positive; steeper than 1;
Y-interce
4.
ppt is 1.
Line c is the best choice.
slope is p5. oositive; less steep than 1;
Y-intercept is -1.
Liine b is the best choice.
slope is positive; 6. ssteeper than 1;
Y-intercept is 0.
Line d is the bbest choice.
slope is positive; steeper than 7. 11;
Y-intercept is 0.
Line h is the best choice.
8.. slope is positive; less steep than 1;
Y-interceept is 3.
Line f is the best choice.
slope is 9. ppositive; equal to 1;
Y-intercept is 0.
Line g iss the best choice.
slope is negative; equal 10. tto 1;
Y-intercept is –3.
Line e is the best choicce.
Honors Lesson 8H1.
2.
3.
4.
5.
6.
done
or
or
or
done
o
412
13
1015
23
96
32
824
rr
or
or
13
1020
12
1824
34
7.
8.
3
2
4
aLGeBra 1
Honors Lesson 9H - Honors Lesson 11H
soLutions316
Honors Lesson 9H1. X is greater than and less than
so C
,11 20
2 = ..
.$ .
75
2 75 1233 00
0
X
CC
X is greater than an
= ( )=
2. dd less than so
so C X
C
C
Cost
,
$ .
10
3
3 5
15 00
== ( )=
3. oof reams
Cost of reams
$ . $ .
$
10 3 00 10 30 00
20 2
= × == .. $ .50 20 50 00× =
This shows that we can use the lowwest
price category
reams
Let
.
$ . $ .50 00 2 50 20÷ =4. arg ,
.
F Finance ch e and B Balance
F B if B
= =
= >008 10000012 1000 50
1 50 00 0
F B if BF if BF if B
= ≥ ≥= > >= =
.
55.
6.
F B
F
F
The lowest possi
== ( )=
.
. $
$ .
012
012 600
7 20
bble ch e if the balance
is over is
arg
$ $1000 10000 01 008 8 00. . $ .
.
× =( )rounded If the balance were $ ,
arg $ . ,
under
the ch e would have been
50
1 00
sso it must have been between
and
$ .
$ .
50 00
1000 000
7 00 0127 00 012
583 33
.
$ . .$ . .
$ .
= ×== ( )
BB
B rounded
÷
7.. Let P Pay and H Hours
P H for all hours und
.= =
= 10 eerP H for all hours overP H for ho
..
4015 4020
== lliday hours
P H
P
P
.
$
8.
9.
== ( )=
( ) + (
10
10 40
400
40 10 5 15)) + ( ) =+ + =
− =
6 20
400 75 120 595
580 400 180
$
$ $ $10. in oveertime pay
hours overtime
re
.
$ $ ;180 15 12
12 40
÷ =+ ggular hours worked= 52 .
Honors Lesson 10HY
1200
1000
800
600
400
200 X
1 2 3 4
1.
2. Y
–5
–2
–3 –4
–1
4
3
2
1
5
X 1 2 3 4 5 6 7 8 9 10
Honors Lesson 11H
1.
aLGeBra 1
Honors Lesson 11H - Honors Lesson 13H
soLutions 317
2. slopeY Y
X X
This is not
=−−
−−
= =
2 1
2 1
400 505 0
3505
70
tthe slope that you will get
from a quick observvation of the graph
member that you used tw
.
Re oo different
scales for X and Y axes
Y mX b
.- -
3. = +50 == ( ) +
== +
= +
= ( ) +=
70 0
5070 50
70 50
70 30 50
2
b
bY X
G T
V
V
4.
5.
,,
$ ,
int ,
100 50
2 150
10 50
+=
( )V
start with po s an6. dd
slope
Y mX b
,15 80
80 5015 10
305
6
50 6 10
( )= −
−= =
= +( ) = (( ) +
= +− =
= −= −
= ( ) −=
b
bb
Y XG T
GG
50 6010
6 106 10
6 12 1072
7.−−
=
= −== ( )
1062
90 6 10100 6
16 67
G
TT
T rounded
8.
.
2. slopeY Y
X X
This is not
=−−
−−
= =
2 1
2 1
400 505 0
3505
70
tthe slope that you will get
from a quick observvation of the graph
member that you used tw
.
Re oo different
scales for X and Y axes
Y mX b
.- -
3. = +50 == ( ) +
== +
= +
= ( ) +=
70 0
5070 50
70 50
70 30 50
2
b
bY X
G T
V
V
4.
5.
,,
$ ,
int ,
100 50
2 150
10 50
+=
( )V
start with po s an6. dd
slope
Y mX b
,15 80
80 5015 10
305
6
50 6 10
( )= −
−= =
= +( ) = (( ) +
= +− =
= −= −
= ( ) −=
b
bb
Y XG T
GG
50 6010
6 106 10
6 12 1072
7.−−
=
= −== ( )
1062
90 6 10100 6
16 67
G
TT
T rounded
8.
.
Honors Lesson 12H1.
2.
3.
C M
C M or C
plan C
= += + =
= ( )
.
.
15 20
0 30 30
1 15 80: ++ ( )= +=
= ( )
40 2
12 4052
2 60 2
$
$
days
CC
plan days
Pl
: C
aan is cheaper
Y Y
X X
X
.1
5100
120
2 00
1
2 1
2 1
4.
5.
=
−−
−−
=220
2 20 1
40
( ) = ( )=
X
X ft
1.
2.
3.
C M
C M or C
plan C
= += + =
= ( )
.
.
15 20
0 30 30
1 15 80: ++ ( )= +=
= ( )
40 2
12 4052
2 60 2
$
$
days
CC
plan days
Pl
: C
aan is cheaper
Y Y
X X
X
.1
5100
120
2 00
1
2 1
2 1
4.
5.
=
−−
−−
=220
2 20 1
40
( ) = ( )=
X
X ft
Honors Lesson 13H1. X Y
Y XY X
− =− = − +
= −
22
2
(Try a sample set of points tto see
which side of the line to shade.)
2. X Y+ = 6YY X
yes
= − + 6
3.
1
2
1 - 3
4. 2 22 2
2 2
X YY XY X
Original problem was ineq
− =− = − +
= −uuality only
so line is dotted
X YY X
,
.
5. 3 63 6
+ == − +
66. no
aLGeBra 1
Honors Lesson 13H - Honors Lesson 14H
soLutions318
4
4 – 6
5
7. A BA B
AB
≥≤
≥≥
2200 500 10 000
52
+ ,
8. See graph only the final answer has b; eeen
shaded here The shaded side of each line.
.is indicated by the small arrows
9. 20 A's and 5 B's is one possible solution
Answers will
.
vvary.
B ≥ 2
10 20 30 40 50 60
A ≥ 2B A ≥ 5B
10
25
20
15
5
a
200A + 500B ≤ 10,000
Honors Lesson 14H1. 8 96 1
12896
996
896
.ft in can be written as=
>
,, .so no
X
X
X in or f
2. 10 112
1 10 12
120 10
=
( ) = ( )( )= tt
L WL W W
W W W
W W W
3. = ++ =
+( ) + =+ + =
=
32 2 4 5
2 3 2 4 5
2 6 2 4 56
.
.
...5
1212 3
15
12 4212 4 4248 42
WW
LL
B TBB
== ( ) +=
= +=
8 96 112
896
996
896
.ft in can be written as=
>
,, .so no
X
X
X in or f
2. 10 112
1 10 12
120 10
=
( ) = ( )( )= tt
L WL W W
W W W
W W W
3. = ++ =
+( ) + =+ + =
=
32 2 4 5
2 3 2 4 5
2 6 2 4 56
.
.
...5
1212 3
15
12 4212 4 4248 42
WW
LL
B TBB
== ( ) +=
= += ( ) += +
4.
BB
B T
B
BB
=
= += ( ) += +=
90
90 000
12 42
12 5 42
60 42102
10
$ ,
$
5.
22 000
12 42126 12 42
84 122000 7 2007
,
6. B TTT
= += +=
+ =
7.
8. Any answer close to would be ok$ , .5 000
aLGeBra 1
Honors Lesson 15H - Honors Lesson 17H
soLutions 319
Honors Lesson 15H1. T S
T S
S T
T T
+ =+ =
= −+ −( ) =
62 482 87 98
62 48
2 62 48 87 9
.
.
.
. . 88
62 48 87 9825 50
10 5 8520 8 158
5 8
TT
C PC P
P
+ ==
+ =+ =
=
. ..
2.
55 1017 2
20 8 17 2 158
20 136 16 1584
−= −
+ −( ) =+ − =
=
CP C
C C
C CC 222
5 50
22
2 2 3 4 754 2
C per bag
N PN P
P P
=
+ == −
−( ) + =−
$ .
.
3.
PP PPP
W W
+ =+ =
=
− = −
3 4 754 4 75
75
180 3 150 2
.
.$. per pen
4.
330 = ( )=
W weeks
L number of people working two y
5. eears
or lessM number of people working
more th
=aan two years
L ML M
M L
L
+ =+ =
= −+
70010 15 8500
700
10 15 7000 8500
10 10500 15 85005 2000
400
3
−( ) =+ − =
− = −=
L
L LLL
X6. ==
==
14
2
12 26
4 24
5 30
6 36
Y
X YX Y
,
,
,
(Answers wiill vary. The second number
will be six times tthe first.)
aan two years
L ML M
M L
L
+ =+ =
= −+
70010 15 8500
700
10 15 7000 8500
10 10500 15 85005 2000
400
3
−( ) =+ − =
− = −=
L
L LLL
X6. ==
==
14
2
12 26
4 24
5 30
6 36
Y
X YX Y
,
,
,
(Answers wiill vary. The second number
will be six times tthe first.)
Honors Lesson 16H1.
2.
3.
C N
R N
C RN N
= +=
=+ =
=
. $
.
. ..
12 2000
62
12 2000 622000 662 122000 50
4 000
1 19 95
N NN
N
Plan a mont
−==
..
,
.4. : hh
for any number of hours
Plan . $ .
:2 4 95 2 2 8+ × = 9954 95 2 6 16 95
4 95 2 10 24 954 95 2 14
. $ .. $ .. $
+ × =+ × =+ × = 332 95
19 95 4 95 2
19 95 4 95 219 95
.
$ . ; .
. ..
5.
6.
C C H
H
= = +
= +−− =
==
4 95 215 27 5
.
.
HH
H
If you use the Internet more .
,
than
hours per month then Plan is bett
7 5
1 eer.
Honors Lesson 17H1. Hometown F C
AmeriBank F C
:
:
.
.
= + −( )= + −
10 10 50
8 12 500
10 10 50 8 12 50
10 10 5 8 12
( )+ −( ) = + −( )
+ − = + −2. . .
. .
C C
C C 665 10 2 12
3 02150
10 10 6
+ = +==
= +
. ..
.
C CC
C
Hometown F3. : 00
16
8 12 60
15 20
( )=
= + ( )=
F
AmeriBank F
F
AmeriBan
$
.
$ .
:
kk s program would be cheaper
C S
C
' .
,4.
5.
= +30 000 75
== + ( )= +=
30 000 75 2000
30 000 150 000
180 000
150
,
, ,
,
C
C
aLGeBra 1
Honors Lesson 17H - Honors Lesson 18H
soLutions320
Hometown F C
AmeriBank F C
:
:
.
.= + −10 10 50
8 12 500
10 10 50 8 12 50
10 10 5 8 12
( )+ −( ) = + −( )
+ − = + −2. . .
. .
C C
C C 665 10 2 12
3 02150
10 10 6
+ = +==
= +
. ..
.
C CC
C
Hometown F3. : 00
16
8 12 60
15 20
( )=
= + ( )=
F
AmeriBank F
F
AmeriBan
$
.
$ .
:
kk s program would be cheaper
C S
C
' .
,4.
5.
= +30 000 75
== + ( )= +=
30 000 75 2000
30 000 150 000
180 000
150
,
, ,
,
C
C
6. ,, ,
,
,
000 30 000 75
120 000 75
1 600
= +==
S
S
S
Honors Lesson 18H1. D number of es
D number of nickelsD nu
==
+ =
dim3
3 4 mmber of quarters
D D DD
DD di
+ + + =+ =
==
3 3 4 187 4 18
7 142 mmes
nickels
quarters
C number o
3 2 6
6 4 10
( ) =( ) + =
=2. ff childrenC number of adultsC number of seni
24
== oors
C C C
C C CC
4 8 2 5 4 1120
4 16 20 112040 112
( ) + ( ) + ( ) =+ + =
= 0028
2 28 56
4 28 112
C children
adults
seniors
=
( ) =( ) =
228 56 112 196+ + =
sin
people
number of bu ess rooms3. === +
Bnumber of coupons rooms B
number
8
of standardd rooms =+( ) = +
=B B
number of senior rooms
8 10 10 80
100 80 10 10 70
45 40 8 50 10 80 35 10
B B
B B B
+( ) − = +
( ) + +( ) + +( ) + BB
B B B B
+( ) =+ + + + + + =
70 8640
45 40 320 500 4000 350 2450 86400
935 6770 8640935 1870
2
2 8
B
BB bu ess
+ ===
( ) + =
sin
110
10 2 80 100
10 2 70 90
tan
coupon
s dard
seni
( ) + =( ) + = oor
rooms occupied
emp
2 10 100 90 202
250 202 48
+ + + =− = tty rooms
T number of
sin
people
number of bu ess rooms3. === +
Bnumber of coupons rooms B
number
8
of standardd rooms =+( ) = +
=B B
number of senior rooms
8 10 10 80
100 80 10 10 70
45 40 8 50 10 80 35 10
B B
B B B
+( ) − = +
( ) + +( ) + +( ) + BB
B B B B
+( ) =+ + + + + + =
70 8640
45 40 320 500 4000 350 2450 86400
935 6770 8640935 1870
2
2 8
B
BB bu ess
+ ===
( ) + =
sin
110
10 2 80 100
10 2 70 90
tan
coupon
s dard
seni
( ) + =( ) + = oor
rooms occupied
emp
2 10 100 90 202
250 202 48
+ + + =− = tty rooms
T number of4. ==
20¢ stamps
T + 5 number off 37¢ stamps
¢ stamps10 5 1
20 3
T number of
T
+( ) =+. . 77 5 0110 5 5 70
20 37 5 10 5 57
T T
T T T
+( ) + +( )( ) =+ +( ) + +( ) =
. .
00
20 37 185 10 50 57067 235 570
67 335
T T TT
T
T fiv
+ + + + =+ =
=
= ee stamps
T ten stamps
T one cent s
20
5 37
100
¢
¢
-
+ == ttamps
W number of womenW number of men
C num
5. =+ =
=1
bber of children
W W CW W C
8 10 1 5 1128 10 10 5
( ) + +( ) + =+ + + ==
+ =
+ + + =+ + =
+ == −
11218 5 102
1 152 1 15
2 1414 2
W C
W W CW C
W CC WW
Substitute W for C in st equation
W
14 2 1
18 5 1
−
+
:
44 2 10218 70 10 102
8 324
1 5
−( ) =+ − =
==
+ =
WW W
WW women
W menn
children
Let X st digit an
15 4 5 15 9 6
1
− +( ) = − == ,6. dd Y nd
X YY X X Y
Y X
X Y
=
+ =+ = + +
= +
− + =
2
1010 36 10
9 36 9
9 9 36
++ + ==
=
( )9 9 90
18 126
7
X Y
Y
Y
1st eq. multiplied by 9
seccond digit
first digit
is 3773
( )− = ( )
−
10 7 3
number337 36=
aLGeBra 1
Honors Lesson 18H - Honors Lesson 20H
soLutions 321
11218 5 102
1 152 1 15
2 1414 2
W C
W W CW C
W CC WW
Substitute W for C in st equation
W
14 2 1
18 5 1
−
+
:
44 2 10218 70 10 102
8 324
1 5
−( ) =+ − =
==
+ =
WW W
WW women
W menn
children
Let X st digit an
15 4 5 15 9 6
1
− +( ) = − == ,6. dd Y nd
X YY X X Y
Y X
X Y
=
+ =+ = + +
= +
− + =
2
1010 36 10
9 36 9
9 9 36
++ + ==
=
( )9 9 90
18 126
7
X Y
Y
Y
1st eq. multiplied by 9
seccond digit
first digit
is 3773
( )− = ( )
−
10 7 3
number337 36=
Honors Lesson 19H 1. t hours
t
= =; b bacteria in thousands
0 3 6 9 12 15 18 21 2241 2 4 8 16 32 64 128 256b
2.
50(in thousands)
bacteria
t (hours) 0 3 6 9 12 15 18 21 24
100
150
200
250
3. t hours
t
= =; b bacteria in thousands
0 1 2 3 4 5 6 7 8 9 10 111 121 2 4 8 16 32 64 128 256 512 1 024 2 048 4 096b , , ,
4.
500
0 1 2 3 4 5 6 7 8 9 10 11 12
1,000
1,500
2,000
2,500
3,000
3,500
4,000
4,500
(in thousands) bacteria
t (hours)
5. The rate of increase increases over time.
Honors Lesson 20H1. x of months mass in grams
xm
= =# ; m
0 1 2 3 4200 100 50 225 12 5
200
1
2
12 5
.
.
2.
3.
4.
5.
g
month
months
g
aLGeBra 1
Honors Lesson 20H - Honors Lesson 22H
soLutions322
6.
x (months) 0 1 2 3 4
100
120
140
160
180
200
20
40
60
80
mass in grams
7. m
m
m g
x= ( )= ( )= ( ) =
200 5
200 5
200 0156 3 125
6
.
.
. .
Honors Lesson 21H1.
2.
3.
done
B A
B
B
B
B
xD= ( )
= ( )= ( )= ( ) =
2
10 2
2
10 64 640
305
6
== ( )= ( )= ( ) =
10 2
10 2
10 4096 40 960
605
12B
B ,
4.
0 10 20 30 40 50 60 t (minutes)
5,000
10,000
15,000
20,000
25,000
30,000
35,000
40,000
45,000
bac
teri
a ce
lls
Honors Lesson 22H1.
2.
never true
sometimes true
:
:
3 19
13
2−
−
=
22
0
9
17
12
15
2 21
2
=
+
= =
3.
4.
never true
never trueX
:
:
≠
55.
6.
7.
always true
never true
alwa
:
:
1 1 0
8 18
1
− =
=−
yys true: a number multiplied by
its reciprocal always equals 1
:
.
8. always true Whenn rai g a power
to a power you multiply
sin
, expoonents
X Y
.
..
9.0 41 52 71 3 52 3 25−−
10.7
aLGeBra 1
Honors Lesson 23H - Honors Lesson 24H
soLutions 323
Honors Lesson 23H1. X Y
0 21 32 53 91 1 52 1 253 1 125
−−−
...
2. 9
-3 -2 -1 1 2 3
3.
4.
5.
They get smaller
They get l er
X Y
.
arg .
0 11 32 933 274 81
1 13
2 19
−
−
6.
1 2 3-3 -2 -1
10
Honors Lesson 24H1.
2.
A X X
A X X
= ( ) +( )= +
( ) + ( ) = +
2 12 2
4 24
4 10 24 10 400 240
2
2==
=
= +( ) −( )
= − + −(
640
1212
1 2 1
12
2 2 1
2
2
ft
A bh
A Y Y
A Y Y Y
3.
))
= + −( )
− +
A Y Y
X X X
X
12
2 1
2 3 7
2
5 4
8
4.
− +
+ − +
+− − +
2 3
2 5 10
6 8
2 3 7 4
4
8 5 4
4
9 5 4
X X
X X X X
X
X X X
5.
XX
X X X X
X
X X
X
−− − + +
−− +
2
2 3 1 4 6
5 7
6 5 7
6
9 5 4
3
4 3
6.
44
2 3
5 3 3 5 3
2 7 3
6 2 21 7 6 23 7
7.
8
X X X
X X X X X X X
+( ) +( ) =+ + + = + +
..
9.
4 3 2 4 8 3 6
8 7 2 3 5
5 2 7 5 2
4 5 3
X X X X X
X X X
+( ) −( ) = − + −
− +
aLGeBra 1
Honors Lesson 24H - Honors Lesson 27H
soLutions324
640
1212
1 2 1
12
2 2 1
= + −( )
− +
A Y Y
X X X
X
12
2 1
2 3 7
2
5 4
8
4.
− +
+ − +
+− − +
2 3
2 5 10
6 8
2 3 7 4
4
8 5 4
4
9 5 4
X X
X X X X
X
X X X
5.
XX
X X X X
X
X X
X
−− − + +
−− +
2
2 3 1 4 6
5 7
6 5 7
6
9 5 4
3
4 3
6.
44
2 3
5 3 3 5 3
2 7 3
6 2 21 7 6 23 7
7.
8
X X X
X X X X X X X
+( ) +( ) =+ + + = + +
..
9.
4 3 2 4 8 3 6
8 7 2 3 5
5 2 7 5 2
4 5 3
X X X X X
X X X
+( ) −( ) = − + −
− +( ) = 66 16 249 7 4X X X− +
Honors Lesson 25H1.
2.
$ , $ .
$ . ,
12 200 800 15 25
19 50 2
÷ =
=
profit per gun
P 0000 3400
39 000 3400
35 600
35 600 2 00
( ) −= −=
P
P
,
$ ,
$ , ,3. ÷ 00 17 80= $ .
cos
per gun
As long as fixed ts remain tthe same
selling more items means more profit
,
cos , ,
per item
fixed ts rent equipm4. = +1 500 1 600 eent
P
+×( ) =
=
100 4 electricity $ ,
.
3 500
19 550 3 500
19 50 800 3 500
12 100
3 500
−= ( ) −=
= +
,
. ,
$ ,
P
P
C NR
5.==
= − +( )= −
= ( ) −=
5
5 3 500
2 500
2 500 500
1 00
N
P N N
P N
P
P
6.
7.
, 00 500 500
2 500
2 2 000 500
4 000 500
− =
= −= ( ) −= − =
$
,
,
8. P N
P
P $$ ,3 500
0 2 500500 2250
250
9. = −==
NN
N
boxes of candy mmust be sold
in order to break even.
1.
2.
$ , $ .
$ . ,
12 200 800 15 25
19 50 2
÷ =
=
profit per gun
P 0000 3400
39 000 3400
35 600
35 600 2 00
( ) −= −=
P
P
,
$ ,
$ , ,3. ÷ 00 17 80= $ .
cos
per gun
As long as fixed ts remain tthe same
selling more items means more profit
,
cos , ,
per item
fixed ts rent equipm4. = +1 500 1 600 eent
P
+×( ) =
=
100 4 electricity $ ,
.
3 500
19 550 3 500
19 50 800 3 500
12 100
3 500
−= ( ) −=
= +
,
. ,
$ ,
P
P
C NR
5.==
= − +( )= −
= ( ) −=
5
5 3 500
2 500
2 500 500
1 00
N
P N N
P N
P
P
6.
7.
, 00 500 500
2 500
2 2 000 500
4 000 500
− =
= −= ( ) −= − =
$
,
,
8. P N
P
P $$ ,3 500
0 2 500500 2250
250
9. = −==
NN
N
boxes of candy mmust be sold
in order to break even.
Honors Lesson 26H1.
2.
P N N
P N
P
= − +( )= −= ( ) −
100 65 18 000
35 18 000
35 1 000
,
,
, 118 000
35 000 18 000
17 000
17 000 1 000
,
, ,
$ ,
$ , ,
P
P
= −=
=3. ÷ $$
, ,
, ,
17
35 2 000 18 000
70 000 18 00
per item
P
P
4. = ( ) −= − 00
52 000
52 000 2 000 26
0 35 18
$ ,
$ , , $5.
6.
÷ == −
per item
N
,,
,
.
000
18 000 35
514 29
515
=( )
N
rounded
items is breaak even po
P N N
P N
P
−= − +( )= −
int
,
,
7. 50 30 10 000
20 10 000
== ( ) −= − =
20 1 000 10 000
20 000 10 000 10 000
10 00
, ,
, , $ ,
$ ,
P
00 1 000 10
50 30 10 000
20
÷ , $
,
== − +( )= −
per case
P N N
P N
8.
110 000
20 2 000 10 000
40 000 10 000 30 00
,
, ,
, , $ ,
P
P
= ( ) −= − = 00
30 000 2 000 15
50
$ , , $
.
÷ =
=
per case
It is more
R N
C
9.
== +
= +
30 10 000
50 30 10 000
2
N
R will equal C when N N
,
,:
00 10 000
500
N
N cases
==
,
1.
2.
P N N
P N
P
= − +( )= −= ( ) −
100 65 18 000
35 18 000
35 1 000
,
,
, 118 000
35 000 18 000
17 000
17 000 1 000
,
, ,
$ ,
$ , ,
P
P
= −=
=3. ÷ $$
, ,
, ,
17
35 2 000 18 000
70 000 18 00
per item
P
P
4. = ( ) −= − 00
52 000
52 000 2 000 26
0 35 18
$ ,
$ , , $5.
6.
÷ == −
per item
N
,,
,
.
000
18 000 35
514 29
515
=( )
N
rounded
items is breaak even po
P N N
P N
P
−= − +( )= −
int
,
,
7. 50 30 10 000
20 10 000
== ( ) −= − =
20 1 000 10 000
20 000 10 000 10 000
10 00
, ,
, , $ ,
$ ,
P
00 1 000 10
50 30 10 000
20
÷ , $
,
== − +( )= −
per case
P N N
P N
8.
110 000
20 2 000 10 000
40 000 10 000 30 00
,
, ,
, , $ ,
P
P
= ( ) −= − = 00
30 000 2 000 15
50
$ , , $
.
÷ =
=
per case
It is more
R N
C
9.
== +
= +
30 10 000
50 30 10 000
2
N
R will equal C when N N
,
,:
00 10 000
500
N
N cases
==
,
Honors Lesson 27H1.
2.
3.
4.
2 2 1
8
2A
not factorable
not factorable
B B
+( )
33 4
3 2 1
0 11 332
+( )
+( ) +( )5.
6.
7.
not factorable
X X
X Y
.
.1111 32 9−−
aLGeBra 1
Honors Lesson 27H - Honors Lesson 28H
soLutions 325
1.
2.
3.
4.
2 2 1
8
2A
not factorable
not factorable
B B
+( )
33 4
3 2 1
0 11 332
+( )
+( ) +( )5.
6.
7.
not factorable
X X
X Y
.
.1111 32 9−−
8. 9
–3 –2 –1 1 2 3
9.
10.
They get smaller They get l er
X Y
. arg .
.0 31 2 522 2 253 2 1251 42 63 10
..
−−−
11. 10
–3 –2 –1 1 2 3
12. They get smaller They get l er. arg .
Honors Lesson 28H1.
2.
2 4 2
2 1 2 2 1 2 1 2
3
3 2
2 2
X X X
X X X X X
A
− + − =
−( ) + −( ) = −( ) +( )33 2
2 2
6 2
3 2 1 2 2 3 1
2
− − +
− − +( ) + − +( ) = − +( ) − +( )A A
A A A A A
B3. 33 2
2 2
4
3 2 3
2 3 2 3 1 2 3
2 4
+ + + =
+( ) + +( ) = +( ) +( )+
B B
B B B B B
X4. XX X
X X X X X
Y Y
3
3 3
2
3 6
2 2 3 2 2 3 2
4 6 2
− − =
+( ) − +( ) = −( ) +( )+ −5. YY
Y Y Y
Y Y Y
Y Y
− =
− + − =−( ) + −( ) =
+( ) −( )
3
4 2 6 3
2 2 1 3 2 1
2 3 2 1
2
6.. 6 6 14 14
6 1 14 1
6 14
4 3 2
3
3
P P P P
P P P P
P P P
− + − =
−( ) + −( ) =+( ) −−( ) = +( ) −( )
+ −+ −
⋅ ++
=
1 2 3 7 1
2
2 3
3
2
2
3 2
2 2
P P P
X X X
X X
X
X X7.
XX X XX X
XX X
X XX X
2
2
23 1
32
21 2
+ −( )+( ) −( ) ⋅ +
+( ) =
+ −−( ) +
( )(( ) =
+( ) −( )−( ) +( ) = =
+− +
+
X X
X X
X
X X
X X
2 1
1 2
11
1
5
3 2
32
28. ÷
XX X X
XX X
X X XX X
XX
3 2
2
6
51 2
63
51
− −=
++( ) +( ) ⋅ − −( )
−( ) =
++( )) +( ) ⋅ +( ) −( )
−=
+X
X XX
X X
X X
X
22 3
3
5 3
1 3
5
aLGeBra 1
Honors Lesson 28H - Honors Lesson 30H
soLutions326
YY
Y Y Y
Y Y Y
Y Y
− =
− + − =−( ) + −( ) =
+( ) −( )
3
4 2 6 3
2 2 1 3 2 1
2 3 2 1
6.. 6 6 14 14
6 1 14 1
6 14
4 3 2
3
3
P P P P
P P P P
P P P
− + − =
−( ) + −( ) =+( ) −−( ) = +( ) −( )
+ −+ −
⋅ ++
=
1 2 3 7 1
2
2 3
3
2
2
3 2
2 2
P P P
X X X
X X
X
X X7.
XX X XX X
XX X
X XX X
2
2
23 1
32
21 2
+ −( )+( ) −( ) ⋅ +
+( ) =
+ −−( ) +
( )(( ) =
+( ) −( )−( ) +( ) = =
+− +
+
X X
X X
X
X X
X X
2 1
1 2
11
1
5
3 2
32
28. ÷
XX X X
XX X
X X XX X
XX
3 2
2
6
51 2
63
51
− −=
++( ) +( ) ⋅ − −( )
−( ) =
++( )) +( ) ⋅ +( ) −( )
−=
+( ) −( )+( ) −( ) = +(
XX X
X
X X
X X
X
22 3
3
5 3
1 3
5))+( )X 1
Honors Lesson 29H1. d vt t
t t
t t
t t
t
= += += +
+ − =−(
16
96 16 16
12 2 2
2 2 12 0
2 4
2
2
2
2
)) +( ) == = −
− =
t
t t
makes no sense so t
3 0
2 3
3 2
,
, secoonds
so the rock was dropped
from
2. 77 3 80
80
+ = ,
fft above the water
d vt t
t t
t t
= += += +
16
80 8 16
10 2
2
2
2
2
tt t
t t
t
2 10 0
2 5 2 0
2 5 2
2 5
+ − =+( ) −( ) =
= −
−
. ,
. makes no seense, so t 2 seconds=− =3. 2000 80 1920
so dis cetan wwas ft
d vt t
t t
t t
t
,1 920
16
1920 32 16
120 2
2 2
2
2
2
= += += +
++ − =+( ) −( ) =
= −
−
2 120 0
12 10 0
12 10
12
t
t t
t
makes no s
,
eense so t onds
d vt t
d
, sec=
= +
= ( ) + ( )
10
16
10 4 16 4
2
2
4.
dd
dd ft
= + ( )= +=
40 16 16
40 256296
,
fft above the water
d vt t
t t
t t
= += += +
16
80 8 16
10 2
2
2
2
2
tt t
t t
t
2 10 0
2 5 2 0
2 5 2
2 5
+ − =+( ) −( ) =
= −
−
. ,
. makes no seense, so t 2 seconds=− =3. 2000 80 1920
so dis cetan wwas ft
d vt t
t t
t t
t
,1 920
16
1920 32 16
120 2
2 2
2
2
2
= += += +
++ − =+( ) −( ) =
= −
−
2 120 0
12 10 0
12 10
12
t
t t
t
makes no s
,
eense so t onds
d vt t
d
, sec=
= +
= ( ) + ( )
10
16
10 4 16 4
2
2
4.
dd
dd ft
= + ( )= +=
40 16 16
40 256296
Honors Lesson 30HYou may also use the unit multiplier method
to gget your answer Either method is fine. .
1. 300 1× 88 5 400
5 400 12 450
==,
,
in
ft
This can also be figur
÷
eed by writing in
as ft and multiplying. .
18
1 5
2.. 50 1 5 75
30 1 5 45
1
× =× =
.
.
#
ft ft
ft ft
length from
, ,
=
× × ==
×
450
450 75 45 1 518 750
1 5
5
3
ft
ft
pace ft3.
11000 5000=m
ft in Roman mile
It is shorter than ood .
, , , ,
, ,
ern mile
4. 5 280 5 280 27 878 400
28 000 000
× =
,
ft rounded
one acre ft from text
2
243 560
28
( )= ( )
,, , ,000 000 43 560 643÷ = ( )mornings rounded
a yard5.
6.. 18 2 36× =in in
This is the number of inches shorrt
his measure is
in ft
ft actual
.
36 3
18 3 15
=− = = length of room
7. Answers will vary.
You may also use the unit multiplier method
to gget your answer Either method is fine. .
1. 300 1× 88 5 400
5 400 12 450
==,
,
in
ft
This can also be figur
÷
eed by writing in
as ft and multiplying. .
18
1 5
2.. 50 1 5 75
30 1 5 45
1
× =× =
.
.
#
ft ft
ft ft
length from
, ,
=
× × ==
×
450
450 75 45 1 518 750
1 5
5
3
ft
ft
pace ft3.
11000 5000=m
ft in Roman mile
It is shorter than ood .
, , , ,
, ,
ern mile
4. 5 280 5 280 27 878 400
28 000 000
× =
,
ft rounded
one acre ft from text
2
243 560
28
( )= ( )
,, , ,000 000 43 560 643÷ = ( )mornings rounded
a yard5.
6.. 18 2 36× =in in
This is the number of inches shorrt
his measure is
in ft
ft actual
.
36 3
18 3 15
=− = = length of room
7. Answers will vary.
aLGeBra 1
Honors Lesson 31H - Honors Lesson 34H
soLutions 327
Honors Lesson 31H
1.
2.
3.
4.
5.
6.
7.
8.
You may also have used the unit multipler
method to get your answer. Either method
is fine unless the directions specified using
unit multipliers.
20,000 3 60,000 mi
60,000 8 480,000 furlongs
1,920 ÷ 4 480 chains
480 ÷10 48 furlongs
48 ÷8 6 mi
1 furlong 10 chains
10 4 40 rods
1 mi 8 furlongs1 mi
10 chains1 furlong
22 yd1 chain
3 ft1 yd
5,280 feet
14 pounds in a stone
14 2 28 pounds in a quarter
28 4 112 pounds in a hundredweight
112 20 2,240 pounds in a ton
heavier than an American ton
6,400 lb ÷8 800 gallons
800 gallons ÷2 400 pecks
400 pecks÷ 4 100 bushels
6,400 ÷2,240 2.86 tons rounded
12
bushel 2 pecks
2 pecks 2 4 gal
4 gal 8 32 lb
( )
× =× ===
==
× =
× × × ×
=
× =× =× =
==
==
=
× =× =
Honors Lesson 32H1.
2.
2 1 008 16 00 18 02
22 0 1 008
. . .
. .
( ) + = ( )+
amu rounded
++ + ( ) =( )
+ =
12 0 3 16 00
83 0
1 008 35 5 3
. .
.
. .
amu rounded
3. 66 5
12 0 2 16 00 44 0
.
. . .
amu rounded
amu
( )+ ( ) =4.
5. hydroocholoric acid:
car
36 5 1 67 10 6 10 1024 23. . .× × = ×− − g
bbon dioxide:
44 0 1 67 10 7 35 10
4 12
24 23. . .
.
× × = ×− − g
6. 00 10 1 008 16 00 74 08
74 08 1 67 10 24
( ) + ( ) + =
× × =−
. . .
. .
amu
11 24 10 22. × − g
Honors Lesson 33H1.
2.
225 16 14
1
888 256 3
÷
÷
=
=
remainder 1
remainder
E
1120
remainder 8120 16 7
378
5 256 1 280
7 256
÷ =
× =×
3.
4.
,
++ × =5 16 1 872,
5. A little bit of red, a little bit of green,
and a lot of blue: since the amountss
of red and green are insignificant, the
resultt is blue.
Remember that we are mixing
6. FFFFFF
llight,
not paint, so white is all colors
mixed together.
7. blue green−
Honors Lesson 34HEach step was rounded u g significant digitssin .
11. P
P
P A U
2 3
2
11 8
1640
1640 40 5
40 5 365 14
=
=
= =× =
.
. . .
. ,, .
, sin .
782 5
14 800
=days u g sig digits
Most stu2. ddents know that Pluto is the
furthest former( ) ,planet from the sun
and that Mercury is closerr to earth
Since this planet has an orbit siz
.
ee less
than it must be closer to the sun th,1 aan
the earth So the answer is Mercury
P
. .
.3. 2 1= 888
6 64
6 64 2 58
2 58 365 942
3
2P
P A U
days u
=
= =× =
.
. . . .
. s iin .
.
.
.
g sig digits
P
A
A
4. =
=
=
100 365 274
274
075
2 3
3
÷ ≈
AA A U
mi
mi
=
× × = ×
×
. . .
. . .
.
422
422 9 3 10 3 925 10
3 9 10
7 7
7 lles using sig. digits
aLGeBra 1
Honors Lesson 35H - Honors Lesson 35H
soLutions328
Honors Lesson 35H1. 2 3 1 200
2 1 200 3
1 200 32
1 200 32
L W
L W
L W
A W
+ == −
= −
= −
,
,
,
,
( )
= − +
= − +
= −( ) −
W
W W
W W
h
3 1 2002
32
600
600
2 32
2
2
,
= −−
=
= − ( ) + ( )
= −
6003
200
3 200 1 200 2002
120 0
2
k ,
, 000 240 0002
120 0002
60 000
60 000 200 300
2
+
= =
=
,
, ,
,
ft
f÷ tt
ft ftdimensions with maximum area: 200 300×
2. 22 2 1 200
2 1 200 3
600
600 2
L W
L W
L W
A W W W
+ == −= −
= −( )( ) = − +
,
,
6600
6002 1
300
300 600 300
90 000 1
2
W
h
k
=−( ) =
= − ( ) + ( )= − +, 880 000 90 000
90 000 300 300
2, ,
,
=
=
ft
dimensions wi
÷ ft
tth maximum area: 300 300ft ft×
test 1 - test 3 329aLGeBra 1
Test 11.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
A: addition
A: addition
C: both associative and
commutative properties
B: 8
D: 2
D: 20
A: 16
B: 3
A: 5
E: 2A 5C
E: 5X Y
B: 10A 2B
A: 2 2 2 2 2
C: 2 2 5 5
D: 36 2 2 3 3
42 2 3 7
2 3 6
−−
−
−++−
× × × ×× × ×
= × × ×= × ×
× =
Test 21.
2.
3.
4.
5.
6.
7.
8.
9.
A: 3 5 2 3 5 4 12
E: 6 4 ÷ 4 36 1 37
A: 10 1 2 1 100 3 1 300 1 299
B: 3 1 1 3 1 1 3 1 2
D: 16 ÷2 1 3 8 3 5
E: A 5 25÷5 2 5 5 4 6
B 5 25 ÷5 2 30 ÷5 4 6 4 2
C 5 25 ÷ 5 2 30 ÷ 5 4 30 ÷1 30
D 5 25÷5 2 5 5 4 14
E 5 25 5 2 5 125 4 126
C: A 3 ÷3 6 9 ÷3 6 3 6 3
B 3 ÷3 5 9 ÷3 5 3 5 8
C 3 ÷3 5 9 ÷3 5 3 5 2
D 3 ÷3 4 9 ÷3 4 3 4 7
E 3÷3 5 1 5 6
B: 4A 5B 3C
A: 0 4 4 4
2
2
2
2 2
2
2
2
2
2
2
2
2
2
( )
( )
( )( ) ( )
( )( )
( )
( )
+ + = + + =
+ = + =
× + − = × − = − =
× − = × − = − =− × = − =
= + − = + − == + − = − = − =
= + − = − = =
= + + = + + == + × − = + − =
= − + = − + = − + =
= + = + = + =
= − + = − + = − + =
= − + = + = + == + = + =− +− = − =
Test 2
10.
11.
12.
13.
14.
15.
E: 6 10 2 6 6
C: 2 8 2 8 6 2 64
36 62
36 62 98
A: A 5 6 5 5 30 25 25
B 5 6 5 1 5 5 5
C 5 5 6 25 6 19 19
D 6 6 5 6 30 24 24
E 5 5 6 5 1 5 5
E : 8 2 2 210 2 5
LCM 2 2 2 5 40
A
D
2 2 2( ) ( )
( )( )
( )
− − = − =
− + − = − + −= + −= + =
= − × = − = − == − × = − × = − =
= × − = − = == − × = − = − == × − = × − = − =
= × ×= ×= × × × =
Test 31.
2.
3.
4.
5.
6.
B: 3X 2 5X 3 8 92X 1 17
2X 18X 9
A: 3D 3 8 D D 9 9 13D 5 17
3D 12D 4
C: 6 2 3B 4 2 4 1 1
3B 9B 3
B: 2 5 2 5 5 8
10 2 25 8 25
D: 3 7 3 10
10 9 10
10 1 10
B: 5Q 9 6 1 25
5Q 15 25
5Q 10
Q 105
Q 2
2( )( )
( ) ( )
( ) ( )( ) ( )
( )
( )
( )
− + + − = +− =
==
− + + − = + −+ =
==
− + + + = + −==
− + + + =− + + + =
+ × − =− =− = −
− − = − ×− = −
= −
= −
= −
ΨΨΨΨΨΨΨΨΨΨΨΨΨΨΨΨΨΨΨΨΨΨΨΨΨΨΨΨΨΨΨΨΨΨΨΨΨΨΨΨΨ10.Ψ10.
11.Ψ11.
12.Ψ12.
E:ΨE: 6Ψ 6 6Ψ 6 10Ψ10 2 6Ψ2 62 6Ψ2 62 6Ψ2 6 6Ψ6
C:ΨC: 2 8Ψ2 8 6 2Ψ6 26 2Ψ6 26 2Ψ6 2 64Ψ64
36Ψ36 62Ψ62
36Ψ36 62Ψ62 98Ψ98
A:ΨA: AΨA 5 6 5Ψ5 6 5 5 3Ψ5 30 2Ψ0 20 2Ψ0 20 2Ψ0 25 2Ψ5 25 2Ψ5 25Ψ5
B 5ΨB 5B 5ΨB 5 6 5Ψ6 5 1 5Ψ1 5 5 5Ψ5 55 5Ψ5 5
C 5ΨC 5C 5ΨC 5 5 6Ψ5 6 25Ψ25 6 1Ψ6 16 1Ψ6 16 1Ψ6 19 1Ψ9 19 1Ψ9 19Ψ9
2Ψ2 2Ψ2 2Ψ26 2
26 2Ψ6 2
26 2( )Ψ( )2 8( )2 8Ψ2 8( )2 8 ( )Ψ( )6 2( )6 2Ψ6 2( )6 2
( )Ψ( )B 5( )B 5ΨB 5( )B 5 6 5( )6 5Ψ6 5( )6 5
( )Ψ( )C 5( )C 5ΨC 5( )C 5 5 6( )5 6Ψ5 6( )5 6
− −Ψ− −10− −10Ψ10− −10 2 6= −2 6Ψ2 6= −2 62 6= −2 6Ψ2 6= −2 6 =Ψ=
− +Ψ− +− +Ψ− +( )− +( )Ψ( )− +( )2 8( )2 8− +2 8( )2 8Ψ2 8( )2 8− +2 8( )2 8 − =Ψ− =− =Ψ− =2 8− =2 8Ψ2 8− =2 8 6 2− +6 2Ψ6 2− +6 26 2− +6 2Ψ6 2− +6 2( )− +( )Ψ( )− +( )6 2( )6 2− +6 2( )6 2Ψ6 2( )6 2− +6 2( )6 2−Ψ−= +Ψ= += +Ψ= += +Ψ= +36= +36Ψ36= +36 −Ψ−= +Ψ= +36= +36Ψ36= +36 =Ψ=
= −Ψ= −= −Ψ= −5 6 5= −5 6 5Ψ5 6 5= −5 6 5× = −Ψ× = −× = −Ψ× = −× = −Ψ× = −5 6 5× = −5 6 5Ψ5 6 5× = −5 6 5 5 3× = −5 3Ψ5 3× = −5 30 2= −0 2Ψ0 2= −0 20 2= −0 2Ψ0 2= −0 25 2=5 2Ψ5 2=5 2
B 5= −B 5ΨB 5= −B 5B 5= −B 5ΨB 5= −B 5( )= −( )Ψ( )= −( )B 5( )B 5= −B 5( )B 5ΨB 5( )B 5= −B 5( )B 5 × =Ψ× =× =Ψ× =6 5× =6 5Ψ6 5× =6 5 − ×Ψ− ×1 5− ×1 5Ψ1 5− ×1 5 = −Ψ= −= −Ψ= −5 5=5 5Ψ5 5=5 5
C 5= ×C 5ΨC 5= ×C 5C 5= ×C 5ΨC 5= ×C 5( )= ×( )Ψ( )= ×( )C 5( )C 5= ×C 5( )C 5ΨC 5( )C 5= ×C 5( )C 5 − =Ψ− =− =Ψ− =5 6− =5 6Ψ5 6− =5 6 − =Ψ− =6 1− =6 1Ψ6 1− =6 16 1− =6 1Ψ6 1− =6 19 1=9 1Ψ9 1=9 1ΨTest Solutions
aLGeBra 1
test 3 - test 4
soLutions330
7.
8.
9.
10.
11.
12.
13.
14.
15.
E: 3 Y Y 6 2 6 72Y 7 13
2Y 20
Y 202
Y 10
E: A. X 3 9; X 9 3 12
B. X 3 9; X 9 3 6
C. 3X 9; X 3
D. X 1 9; X 9 1 8
E. X 1 12; X 12 1 13
E: A. R 2R 15; 3R 15; R 5
B. 2R 3 15; 2R 12; R 6
C. R 2R 18; 3R 18; R 6
D. R 5R 15; 6R 15; R 156
2 12
E. R 5R 6; 6R 6; R 1
A: I. 3Q 4 20; 3Q 24; Q 8
II. 4Q 3 17; 4Q 20; Q 5
III. 4Q 3 23; 4Q 20; Q 5
IV. 4Q 3Q 21; Q 21
A: 5 P 3 3 6 5P
P 2 18 5P2 18 5P P
16 4P4 P
D: 12 34
12 12
12 23
X
9 6 8X15 8X
X 158
178
B: 15 35
Y 15 13
15 15
9Y 5 39Y 8
Y 89
D: 100 .09X 100 1.8 100 2.25
9X 180 2259X 405
X 4059
45
B: 10 .6A 10 15 10 7.2
6A 150 726A 72 1506A 78
A 786
13
3 6 4
3 5 3
( )
( ) ( ) ( )
( ) ( ) ( )
( ) ( )
( ) ( ) ( )
( )
− + + − + = +− =
=
=
=
− = = + =+ = = − == =
+ = = − =− = = + =
+ = = =+ = = =
+ = = =
+ = = = =
+ = = =
− = = =− = = =+ = = =− = =
+ − = ++ = +
− = −− =− =
+ =
+ ==
= =
− =
− ==
=
− =− =
=
= =
+ =+ =
= −= −
= − = −
7.
8.
9.
10.
11.
12.
13.
14.
15.
E: 3 Y Y 6 2 6 72Y 7 13
2Y 20
Y 202
Y 10
E: A. X 3 9; X 9 3 12
B. X 3 9; X 9 3 6
C. 3X 9; X 3
D. X 1 9; X 9 1 8
E. X 1 12; X 12 1 13
E: A. R 2R 15; 3R 15; R 5
B. 2R 3 15; 2R 12; R 6
C. R 2R 18; 3R 18; R 6
D. R 5R 15; 6R 15; R 156
2 12
E. R 5R 6; 6R 6; R 1
A: I. 3Q 4 20; 3Q 24; Q 8
II. 4Q 3 17; 4Q 20; Q 5
III. 4Q 3 23; 4Q 20; Q 5
IV. 4Q 3Q 21; Q 21
A: 5 P 3 3 6 5P
P 2 18 5P2 18 5P P
16 4P4 P
D: 12 34
12 12
12 23
X
9 6 8X15 8X
X 158
178
B: 15 35
Y 15 13
15 15
9Y 5 39Y 8
Y 89
D: 100 .09X 100 1.8 100 2.25
9X 180 2259X 405
X 4059
45
B: 10 .6A 10 15 10 7.2
6A 150 726A 72 1506A 78
A 786
13
( )
( ) ( ) ( )
( ) ( ) ( )
( ) ( ) ( )
− + + − + = +− =
=
=
=
− = = + =+ = = − == =
+ = = − =− = = + =
+ = = =+ = = =
+ = = =
+ = = = =
+ = = =
− = = =− = = =+ = = =− = =
+ − = ++ = +
− = −− =− =
+ =
+ ==
= =
− =
− ==
=
− =− =
=
= =
+ =+ =
= −= −
= − = −
Test 41.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
B: 14 2 716 2 2 2 228 2 2 7
GCF 2
B: 14 2 716 2 2 2 224 2 2 2 3
GCF 2
A: 24 2 2 2 336 2 2 3 340 2 2 2 5
GCF 2 2 4
E: 26 2 1352 2 2 1365 5 13
GCF 13
E: 3 A B 6
3A 3B 3 6 3A 3B 18
B: 6 X 2Y 3 Z 6X 12Y 18 6Z
D: 2 3T 5 4T 3
6T 10 8T 6 14T 4
A: A B 4Q 1 AB 4AQ A
B: 10B 2 5 B15B 3 5 B40 2 2 5
GCF 5
E: 36X 2 2 3 3 X12Y 2 2 3 Y24Z 2 2 2 3 ZGCF 2 2 3 12
C: 60A 2 2 3 5 A30D 2 3 5 D
90 2 3 3 5GCF 2 3 5 30
( )
( )( )
( )( )
= ×= × × ×= × ×=
= ×= × × ×= × × ×=
= × × ×= × × ×= × × ×= × =
= ×= × ×= ×=
+ + =+ + = + +
− + + = − + +
− + + =− + + = −+ + = + +
= × ×= × ×= × ×
=
= × × × ×= × × ×= × × × ×= × × =
= × × × ×= × × ×= × × ×= × × =
aLGeBra 1
test 4 - test 6
soLutions 331
12.
13.
14.
15.
C: 18A 24B 30
6 3A 4B 6 5
GCF is 6
B: 15P 25R 35T
5 3P 5R 5 7T
E: 4G 16H 8J 32
4 G 4H 2J 4 8
G 4H 2J 8
B: 9X 27Y 3Z
3 3X 9Y 3 Z
3X 9Y Z
( )
( ) ( )
( )
( )
( )
( )
( )
+ =+ =
− =− =
+ − =+ − =+ − =
+ =+ =+ =
Test 51.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
E: 1, 1
B: 1, 2
C: 3, 1
A: 3, 4
C: 3, 0
D: quadrant IV
A: quadrant I
E: the origin
C: Descartes
D: 0
C: quadrant III
D: 0
C: algebra and geometry
A: They form a straight line.
D: They cannot be connected
with a straight line.
( )( )( )( )( )
− −
−
−
Test5
Test 61.
2.
3.
4.
5.
A: G D 3
C: S 2W 5
B: G 2W 2
C: C 2D 5
C 2 6 5
C 12 5C 17
E: M 10D 8
M 10 12 8 12 days worked
M 120 8M $128
( )
( )
( )
= += += +
= += += +=
= += += +=
Test 6
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
E: Y 4X 1
Y 4 3 1
Y 12 1Y 11
B: A 6B 4
A 6 0 4
A 0 4A 4
E: R T 5
R 2 5
R 3
A: Use trial and error to check all answers. Answer A is the one that yields a true statement:
Y 3X 1
13 3 4 1
13 12 113 13
D: Use the same process as in #9.
Y X 4
6 2 4
6 6
B: 0, 1 :
Y 3X 1
1 3 0 1
1 1
1, 2 :
Y 3X 1
2 3 1 1
2 3 12 2
Both points are tested because it
takes 2 points to define a line.
E: The Y–axis includes all points where X 0.
C: Any 2 points from line S can be chosen.
We show 0, 2 and 2, 0 here :
0, 2 :
Y X 2
2 0 2
2 2
2, 0 :
Y X 2
0 2 2
0 0
The student can try just one point on the
possible answers given until one works,
then the other point can be tested.
B: Use the same process as #11:
0, 4 :
Y 2X 4
4 2 0 4
4 4
1, 2 :
Y 2X 4
2 2 1 4
2 2 42 2
E: The X-axis includes all points where Y 0.
( ) ( )
( ) ( )( ) ( )
( ) ( )
( )
( )
( )
( )
( )
( ) ( )
( )
( )
( )
( )
( ) ( ) ( )
( ) ( )
( ) ( ) ( )
= −= −= −=
= += += +=
= −= −= −
= += += +=
= −− = − −− = −
= += +=
− −= +
− = − +− = − +− = −
=
−
= += +=
−= += − +=
= += +=
−= += − += − +=
=
aLGeBra 1
test 6 - test 9
soLutions332
14.
15.
E: Y 4X 1
Y 4 3 1
Y 12 1Y 11
B: A 6B 4
A 6 0 4
A 0 4A 4
E: R T 5
R 2 5
R 3
A: Use trial and error to check all answers. Answer A is the one that yields a true statement:
Y 3X 1
13 3 4 1
13 12 113 13
D: Use the same process as in #9.
Y X 4
6 2 4
6 6
B: 0, 1 :
Y 3X 1
1 3 0 1
1 1
1, 2 :
Y 3X 1
2 3 1 1
2 3 12 2
Both points are tested because it
takes 2 points to define a line.
E: The Y–axis includes all points where X 0.
C: Any 2 points from line S can be chosen.
We show 0, 2 and 2, 0 here :
0, 2 :
Y X 2
2 0 2
2 2
2, 0 :
Y X 2
0 2 2
0 0
The student can try just one point on the
possible answers given until one works,
then the other point can be tested.
B: Use the same process as #11:
0, 4 :
Y 2X 4
4 2 0 4
4 4
1, 2 :
Y 2X 4
2 2 1 4
2 2 42 2
E: The X-axis includes all points where Y 0.
( ) ( )
( ) ( )( ) ( )
( ) ( )
( )
( )
( )
( )
( )
( ) ( )
( )
( )
( )
( )
( ) ( ) ( )
( ) ( )
( ) ( ) ( )
= −= −= −=
= += += +=
= −= −= −
= += += +=
= −− = − −− = −
= += +=
− −= +
− = − +− = − +− = −
=
−
= += +=
−= += − +=
= += +=
−= += − += − +=
=
Test 71.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
C
D
A
C
D
C: slope is rise over run or 34
A: riserun
22
1
D
B: riserun
23
A: riserun
11
1
E
C: riserun
31
3
E No line crosses the Y-axis at 3.
A The line crosses the Y-axis at –2.
C The line crosses the Y-axis at –3.
( )
( )( )
= =
=
=−
= −
= =
Test 81.
2.
3.
4.
5.
6.
7.
8.
9.
10.
A: P 1 W 3
D: R 10W 50
E: M 5D 4
C: M 4D 5
D: T 3W 4
A: 4
C: 2
E: 12
B: Since the y-intercept is the point
where the X-coordinate is 0, 0, 2 from
the points given is the y-intercept.
The Y-coordinate of that point is 2.
A: slope 31
3
( )
( )= − += − += − += −= − −
−
= =
Test 8
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
A: P 1 W 3
D: R 10W 50
E: M 5D 4
C: M 4D 5
D: T 3W 4
A: 4
C: 2
E: 12
B: Since the y-intercept is the point
where the X-coordinate is 0, 0, 2 from
the points given is the y-intercept.
The Y-coordinate of that point is 2.
A: slope 31
3
( )
= − += − += − += −= − −
−
= =
Y
X
11.
12.
13.
14.
15.
C: slope 3; Y-intercept 2
Y 3X 2
B: slope 11
1
B: slope 21
2
A: slope 0any X
A: slope 11
1
= == +
= =
= − = −
=
= − = −
Test 91.
2.
3.
4.
5.
6.
A: slope
C: parallel
D: slope 21
2
C: slope 11
1
B: slope 13
B: 2Y 6X 4Y 3X 2
divide both sides by 2
slope 3
( )
= =
= =
= −
= += +
=
Test 9
Y
X
#4 #3
#5
1.
2.
3.
4.
5.
6.
A: slope
C: parallel
D: slope 21
2
C: slope 11
1
B: slope 13
B: 2Y 6X 4Y 3X 2
divide both sides by 2
slope 3
( )
= =
= =
= −
= += +
=
Test 9
aLGeBra 1
test 9 - test 11
soLutions 333
7.
8.
9.
10.
11.
12.
13.
14.
15.
A: 3Y 6X 3Y 2X 1
divide both sides by 3
slope 2
A: 3X 2Y 3
E: 6
E: Y 2X 62X Y 62X Y 6
D: 2
D: Y 2X 4
A: line F; intercept is 0, and slope is 1
E: 3
C: 0
( )
= += +
=+ =
= +− + =
− = −
= −−
−
Test 101.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
C: perpendicular
E: none of the above
correct answer would be negative reciprocal
B: slope 24
12
D: 3
D: slope 12
; y intercept 3
Y 12
X 3
A: Y 12
X 3
12
X Y 3
X 2Y 6
C: 2 negative reciprocal of 12
C: slope 42
2
E: Graph the points and connect them, then
note where the line crosses the Y–axis. 0, 1
A: slope 2; y–intercept 1
Y 2X 1
B: Y 2X 12X Y 1
D: 12
E: Y 3X 6 slope must be 3
E: Y 14
X 1 slope must be 14
C: 3Y 6X 123Y 6X 12Y 2X 4
negative reciprocal of –2 is 12
( )
= =
= − =
= +
= +
− + =
− + =
−
= − = −
= − == − +
= − ++ =
= − + −
= −
+ == − += − +
Test10
#9 Y
X
#3
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
C: perpendicular
E: none of the above
correct answer would be negative reciprocal
B: slope 24
12
D: 3
D: slope 12
; y intercept 3
Y 12
X 3
A: Y 12
X 3
12
X Y 3
X 2Y 6
C: 2 negative reciprocal of 12
C: slope 42
2
E: Graph the points and connect them, then
note where the line crosses the Y–axis. 0, 1
A: slope 2; y–intercept 1
Y 2X 1
B: Y 2X 12X Y 1
D: 12
E: Y 3X 6 slope must be 3
E: Y 14
X 1 slope must be 14
C: 3Y 6X 123Y 6X 12Y 2X 4
negative reciprocal of –2 is 12
( )
= =
= − =
= +
= +
− + =
− + =
−
= − = −
= − == − +
= − ++ =
= − + −
= −
+ == − += − +
Test10
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
C: perpendicular
E: none of the above
correct answer would be negative reciprocal
B: slope 24
12
D: 3
D: slope 12
; y intercept 3
Y 12
X 3
A: Y 12
X 3
12
X Y 3
X 2Y 6
C: 2 negative reciprocal of 12
C: slope 42
2
E: Graph the points and connect them, then
note where the line crosses the Y–axis. 0, 1
A: slope 2; y–intercept 1
Y 2X 1
B: Y 2X 12X Y 1
D: 12
E: Y 3X 6 slope must be 3
E: Y 14
X 1 slope must be 14
C: 3Y 6X 123Y 6X 12Y 2X 4
negative reciprocal of –2 is 12
( )
= =
= − =
= +
= +
− + =
− + =
−
= − = −
= − == − +
= − ++ =
= − + −
= −
+ == − += − +
Test 111.
2.
3.
D: slope 3 15 2
23
B: slope 1 02 4
16
16
E: slope 8 24 3
8 24 3
107( )
( )
= −−
=
= −− −
=−
= −
= − −− −
= ++
=
Test11
4.
5.
6.
7.
8.
9.
10.
E: 2X Y 13Y 2X 13
B: 3X 4Y 84Y 3X 8
Y 34
X 2
C: 2X 2Y 6 02Y 2X 6Y X 3
A: 6
B: 2X 3Y 43Y 2X 4
Y 23
X 43
slope 23
D: 4X 2Y 162Y 4X 16Y 2X 8
slope 2
C: a point and the slope or two points
+ == − +
− + == +
= +
− − =− = − +
= −
+ == − +
= − +
= −
− + == += +
=
aLGeBra 1
test 11 - unit test i
soLutions334
11.
12.
13.
14.
B: Y mX b
1 3 2 b
1 6 b1 6 b; b 5
A: Y mX b
2 1 2 b
2 2 b2 2 b; b 4
E: slope 3 16 4
22
1
Y mX b
3 1 6 b
3 6 b3 6 b 3
OR Y mX b
1 1 4 b
1 4 b1 4 b 3
Y X 3
B: slope 6 04 1
65
65
Y mX b
0 65
1 b
65
b
OR Y mX b
6 65
4 b
305
245
b
305
245
b 65
Y 65
X 65
( )
( ) ( )
( )
( )
( ) ( )
( ) ( )( )
( )
( )( )
( )
( )
= += += +
− = = −
= +− = − − +− = +
− − = = −
= −−
= =
= += += +
− = = −
= += += +
− = = −= −
= −− −
=−
= −
= +
= − +
=
= +
= − − +
= +
− = =
= − +
15. A: Slope is 1; this eliminates all but A and C.
using 2, 3 :
3 1 2 5
3 2 53 3
(Either point could have been used.)
( )( ) ( )( )
−
= − += − +=
Unit Test I
1.
2.
3.
3 3 3 9
2 3 1 4 2 9 4 3
3 2 1 4 1 3 1 3 2
2
2
( )− = − × = −
− + − × = − + − =− − − = − − = − = −
I
1.
2.
3.
3X 2 2X 4 X3X 2X X 4 2
6X 6X 1
12
B 13
29
181
12
B 181
13
181
29
9B 6 49B 2
B 29
.03Y 1 4.3
100 .03Y 100 1 100 4.3
3Y 100 4303Y 330
Y 3303
110
( ) ( ) ( ) ( ) ( )( )
− + = −+ + = +
==
+ =
⋅ + ⋅ = ⋅
+ == −
= −
+ =+ =
+ ==
= =
II
1.
1.
2.
3.
1.
2.
Point B
associative
distributive
commutative
see graph
see graph
III
IV
V
Y
X
#1 #2
VI #1
aLGeBra 1
unit test i - test 12
soLutions 335
1. Y 3 2XY 2X 3
slope is –2
Y-intercept is –3
see graph
+ = −= − −
VI
1.
1.
M 3D 2
perpendicular, so slope is 13
Y mX b
1 13
2 b
33
23
b
33
23
b 53
Y 13
X 53
Y–intercept form
13
X Y 53
X 3Y 5 standard form
see graph
( )
( ) ( )
( )
= −
−
= +
= − +
= − +
+ = =
= − +
+ =
+ =
VII
VIII
Y
X
Y = 3X
1. m 4 10 2
32
32
Y mX b
4 32
0 b
4 b
Y 32
X 4 Y-intercept form
32
X Y 4
3X 2Y 8 standard form
Either the Y-intercept form or the
standard form may be considered
correct.
( )
( )( )
( )
= −−
=−
= −
= +
= − +
=
= − +
+ =
+ =
IX
a.
b.
c.
d.
m 3
m 3
Y 3X 7Y 3X 7m 3
3X Y 12Y 3X 12Y 3X 12m 3
a, b and d all have a slope of 3,
so they are parallel
==
+ == − += −
= +− = − +
= −=
X
Test 121.
2.
3.
4.
5.
6.
B: 2Y X 4 because of the > sign
E: 2Y 4X 8; divide both sides by 2:
Y 2X 4
dividing by a negative number changes
the direction of the inequality
B: 3Y 6X 6Y 2X 2
dividing by a positive number does not
change the direction of the inequality
C: sketch graph to determine location
slope is 1 and Y-intercept is – 4
C: II and V
B: 2Y 6X 2
Y 3X 1 see #3( )
> +
− > + −< − −
< −< −
> +> +
Test12
aLGeBra 1
test 12 - test 14
soLutions336
7.
8.
9.
10.
11.
12.
13.
14.
15.
D: slope is 3; Y-intercept is 1; dotted line
E: 4Y 8X 164Y 8X 16
Y 2X 4 see #2
C: slope is 2; Y-intercept is 4; dotted line
D: 3Y 9X ≤ 123Y ≤ 9X 12
Y ≥ 3X 4 see #2
A: slope is 3; Y-intercept is – 4; solid line
B: 3Y 9X ≤ 123Y ≤ 9X 12
Y ≤ 3X 4 see #3
E: slope is 3; Y-intercept is 4; solid line
A: 2Y 6X 2
Y 3X 1 see #2
Y ≤ 3X 4 see #3
B: slope is 3; Y-intercept is 1; dotted line
( )
( )
( )
( )
( )
− + >− > − +
< −−
− +− − +
−
−++
− > +< − −
+
− −
Test 131.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
A: infinite
B: 1
D: the lines intersect
E: " 3, 4 will not satisfy either line"
is a false statement
A: slope 4; Y intercept 2
B: slope 1; Y intercept 3
C: from the graph
E: slope 4; Y intercept 2
B: from the graph
B: slope 1; Y intercept 4
A: slope 1; Y intercept 4
C: slope 4; Y intercept 1
D: slope 4; Y intercept 1
E: from the graph
B: from the graph
( )
= − − = −= − =
= − =
= − − == − = −= − == − − =
Test13
Test 141.
2.
D: substitution
B: Y 2−
Test14
3.
4.
5.
6.
7.
8.
E: Y X 8 Y Y 2 8
2Y 2 82Y 10Y 5
Y X 8 5 X 8
X 8 5X 3
3, 5
E: 8Y X 2X 8Y 2
A: Y 5 X Y 5 8Y 2Y 8Y 2 5
9Y 3
Y 39
13
Y 5 X 13
5 X
13
153
X
143
X 4 23
4 23
, 13
D: substitute to find the other variable
E: the answer may be an estimate
B: X Y 8 X Y 8
2X Y 7 2 Y 8 Y 7
2Y 16 Y 72Y Y 7 16
3Y 9
Y 93
3
X Y 8 X 3 8
X 8 3X 5
5, 3
( )
( )
( )
( )
( )
( )+ = => + − =− =
==
+ = => + == −=
+ == − +
+ = => + = − ++ = −
= −
= − = −
+ = => − + =
− + =
= =
−
+ = => = − +
− = => − + − =− + − =
− − = −− = −
= −−
=
+ = => + == −=
aLGeBra 1
test 14 - test 15
soLutions 337
9.
10.
11.
12.
13.
14.
A: Y X 2
2X Y 14 2X X 2 14
3X 2 143X 12
X 123
4
Y X 2 Y 4 2
Y 6
4, 6
B: Y X 1 Y X 1
2X Y 2 2X X 1 2
3X 1 23X 3X 1
Y X 1 Y 1 1
Y 1 1Y 0
1, 0
B: X 2Y 3
Y 6X 4 Y 6 2Y 3 4
Y 12Y 18 4Y 12Y 22
11Y 22
Y 2211
2
X 2Y 3 X 2 2 3
X 4 3X 1
1, 2
E: 470 ÷55 8.5 hours
6:00 AM 8.5 hours 2:30 PM
D: 470 ÷23.5 20 mpg
D: 36 The numbers are squares of consecutive
counting numbers.
( )
( )
( )
( )
( )
( )
( )
( )
( )
= +
+ = => + + =+ =
=
= =
= + => = +=
− = − => = −
+ = => + − =− =
==
− = − => − = −= − +=
= +
= + => = + += + +
− =− =
=−
= −
= + => = − += − += −
− −=
+ ==
15. C : A 4 0 2Y 12
2Y 12Y 6
B 4 10 2Y 12
40 2Y 122Y 52Y 26
C 4 3 2Y 12
12 2Y 122Y 0
Y 02
0
D 4 1 2Y 12
4 2Y 122Y 8Y 4
E 4 2 2Y 12
8 2Y 122Y 4Y 2
( )
( )
( )
( )
( )
− =− =
= −
− − =− − =
− == −
− =− =− =
=−
=
− =− =− =
= −
− =− =− =
= −
C : A 4 0 2Y 12
2Y 12Y 6
B 4 10 2Y 12
40 2Y 122Y 52Y 26
C 4 3 2Y 12
12 2Y 122Y 0
Y 02
0
D 4 1 2Y 12
4 2Y 122Y 8Y 4
E 4 2 2Y 12
8 2Y 122Y 4Y 2
( )
( )
( )
( )
( )
− =− =
= −
− − =− − =
− == −
− =− =− =
=−
=
− =− =− =
= −
− =− =− =
= −
Test 151.
2.
3.
4.
5.
6.
7.
8.
9.
10.
D: graphing, substitution, or elimination
C: Make sure both are in the same form.
B: 2
E: 4
C: X 3Y 6
X 3Y 12
2X 18
X 9
B: X 3Y 6 9 3Y 6
3Y 6 93Y 3Y 1
D: 9, 1
E:
3X Y 2 4
2X 4Y 1312X 4Y 810X 5
X 12
A: 2X 4Y 13 2 12
4Y 13
1 4Y 134Y 14
Y 144
3 12
A: 12
, 3 12
( )
( )
( ) ( )
−
− =+ =
==
− = => − =− = −− = −
=
+ = − =>+ =
− − = −− =
= −
+ = => − + =
− + ==
= =
−
Test15
aLGeBra 1
test 15 - test 16
soLutions338
11.
12.
13.
14.
15.
C:
X 2Y 4 3
X 6Y 12
3X 6Y 124X 24
X 6
X 6Y 12 6 6Y 12
6Y 12 66Y 6Y 1
6, 1
D: 3X Y 92X Y 3
X 12
X 12
2X Y 3 2 12 Y 3
24 Y 3Y 27
12, 27
E: 6N 4N 8N÷ 4
B: 100
The numbers are squares of
consecutive counting numbers.
D: A 2 0 3Y 6
3Y 6Y 2
B 2 1 3Y 6
2 3Y 63Y 4
Y 43
1 13
C 2 5 3Y 6
10 3Y 63Y 4
Y 43
1 13
D 2 5 3Y 6
10 3Y 63Y 16
Y 163
5 13
E 2 8 3Y 6
16 3Y 63Y 10
Y 103
3 13
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
− = =>+ =− =
==
+ = => + == −==
− − =+ =
− == −
+ = => − + =− + =
=−
− =
+ ===
+ =+ =
=
= =
+ =+ =
= −
= − = −
− + =− + =
=
= =
+ =+ =
= −
= − = −
Test 161.
2.
3.
4.
5.
A: P 5N 28
B:
N D 7 10
.05N .10D .50 100
10N 10D 70
5N 10D 50
5N 20
N 205
N 4
A: N D 7 4 D 7
D 7 4 3
D:
N D 13 5
.05N .10D 1.10 100
5N 5D 65
5N 10D 1105D 45D 9
A: N D 13 N 9 13
N 13 9N 4
( )( ) ( )
( ) ( )( ) ( )
( )
( )
( )
+ =
+ = − =>+ = =>
− − = −+ =
− = −
= −−
=
+ = => + == − =
+ = − =>+ = =>
− − = −+ =
==
+ = => + == −=
Test16
6.
7.
8.
9.
10.
11.
D:
N Q 13 5
.05N .25Q 1.85 100
5N 5Q 65
5N 25Q 185
20Q 120
Q 6
E: N Q 13 N 6 13
N 13 6N 7
A: elimination
B:
D Q 10 25
.10D .25Q 2.05 100
25D 25Q 250
10D 25Q 205
15D 45
D 3
C: D Q 10 3 Q 10
Q 10 3
Q 7
E :
A B 5 30
.30A .75B 2.40 100
30A 30B 15030A 75B 240
45B 90
B 2
( )( )
( )( )
( )( )
( )
( )( )
( )
( ) ( )( ) ( )
+ = − =>
+ = =>
− − = −+ =
==
+ = => + == −=
+ = − =>
+ = =>
− − = −+ =
− = −=
+ = => + == −=
+ = − =>+ = =>
− − = −+ =
==
aLGeBra 1
test 16 - test 19
soLutions 339
12.
13.
14.
15.
B: A B 5 A 2 5
A 5 2A 3
B: Y 15X 50
A: Y 15X 50 Y 15 10 50
Y 150 50Y $200
E: Y 20X 50 Y 20 10 50
Y 200 50Y $250
( )
( )
( )+ = => + == −=
= +
= + => = += +=
= + => = += +=
Test 171.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
B: N, N 1, N 2
C: N, N 2, N 4
C: N, N 2, N 4
D: 6N 2 N 1 N 2 5
C: 6N 2 N 1 N 2 5
6N 2N 2 N 2 56N 2N N 2 5 2
3N 9N 3
A: 6N 5 N 2 3 N 2 10 N 1 10
6N 5N 10 3N 6 10N 10 106N 5N 3N 10N 10 10 10 6
4N 4N 1
B: N 2 1 2 3
C: 3N N 2 2 3 N 4
3N N 2 2 3N 123N N 3N 12 2 2
N 8
E: N 2 8 2 10
D: 10N 10 N 2 10 N 4 10
10N 10N 20 10N 40 1010N 10N 10N 40 10 20
10N 30N 3
second integer N 2 3 2 5
A: 3
( )
( )
( ) ( )( ) ( )
( ) ( ) ( )
( )( ) ( )
( ) ( )
+ ++ ++ +
− + = + +
− + = + +− − = + +− − = + +
==
+ + + + = + ++ + + + = + ++ + − = + − −
==
+ => + =
+ + + = ++ + + = ++ − = − −
=+ => + =
+ + = + ++ + = + +
+ − = + −==
= + = + =
Test17
12.
13.
14.
15.
A: 3N 2 N 2 13 3 N N 4
3N 2N 4 13 3 2N 4
3N 2N 4 13 6N 123N 2N 6N 12 4 13
7N 21N 3
C: N 4 3 4 1
C: 4N 2 N 1 4 N 2
4N 2N 2 4N 84N 2N 4N 8 2
2N 6N 3
C: N 2 3 2 5
[ ]
( )
( )
( ) ( )
( ) ( )
− + + = − + + − − + = − +− − + = − −
− + = − + −= −= −
+ => − + =
+ + = ++ + = +
+ − = −==
+ => + =
Test 18Test181.
2.
E
D
:
:
−( ) = − × −( ) =− = − ×( ) = −
6 6 6 36
6 6 6 36
2
2
33.
4.
5.
A R R R R
B R R R R
E R R
:
:
:
2 4 2 4 6
4 2 4 2 2
8 2
× = =
= =
+
−÷
÷ == =
⋅ = =
=
−
+
R R
B A A A A
C C C D D C
X X X X X
8 2 6
5 3 5 3 8
4 3 2 1
6.
7.
:
: 44 3 2 1 7 3
8 2 8 2 6
144 12
4 4 4 4
+ +
−
=
=
= =
D C D
C
A
C
8.
9.
10.
:
:
:
÷
:
:
X Y X Y X Y X Y
B A A
C B
2 3 4 2 4 3 1 6 4
2
281 9
= =
− = −
=
+ +
11.
12. BB
C
B
A adde
13.
14.
15.
:
: subtracted
:
2 2 4 4 16 42 2 = ⋅ = =
dd
Test 19Test191.
2.
3.
CX
X
DX X
X X X
E X
:
:
:
1
1
33
3 43 4 7
−
− − −
−
=
= =
444
55
2 2 2 2 4
1
5 1
5
8 8 8 8
=
=
⋅ = =
−
− − − + −( ) −
X
E
A
C
4.
5.
6.
:
:
:
:
:
7 7 7 75 3 5 3 8
8 2 8 2 6
2 3
− − − −
−
− −
= =
= =
÷
÷7.
8.
E X X X X
A X X == = =
=
− + −( ) −X XX
B X
2 3 55
0
1
19. :
Any number raised
;
tto the 0 power equals 1.
: − − − + −2 6 3 2 3(( ) + −
− − − + −
6 1 5 7
1 8 7 2 1 8 7 2 9
aLGeBra 1
test 19 - test 21
soLutions340
1.
2.
3.
CX
X
DX X
X X X
E X
:
:
:
1
1
33
3 43 4 7
−
− − −
−
=
= =
444
55
2 2 2 2 4
1
5 1
5
8 8 8 8
=
=
⋅ = =
−
− − − + −( ) −
X
E
A
C
4.
5.
6.
:
:
:
:
:
7 7 7 75 3 5 3 8
8 2 8 2 6
2 3
− − − −
−
− −
= =
= =
÷
÷7.
8.
E X X X X
A X X == = =
=
− + −( ) −X XX
B X
2 3 55
0
1
19. :
Any number raised
;
tto the 0 power equals 1.
: 10. E X Y X Y X− − − + −=2 6 3 2 3(( ) + −
− − − + −( ) + −
=
= =
Y X Y
B A A B B A B A B
6 1 5 7
1 8 7 2 1 8 7 2 911. : 99
4 2
34 2 3 4 2 3 9
3 2
2 4
12.
13.
E B B
BB B B B B
A P N
N P
:
:
−+ +
−
= = =
== = =
( )
− − − + −( ) − + −( ) − −P N N P P N P N
D
3 2 2 4 3 4 2 2 1 4
25
914. : == =
( ) =
⋅9 925 10
15. C X XAB
AB:
Test 20Test 201. A: equation is a specific kind of polynnomial
called a trinomial
: 2. D X X
X X
2
23 2
4
+ ++ + +55
2 7 7
10
2 4
2 14
2
2
2
2
2
X X
A X X
X X
X X
E X
+ +
+ ++ − +
− +
3.
4.
:
: ++ ++ − −
+ +
− −+ − −
8 6
3 1
2 5 5
5 2
4 3
2
2
2
2
2
X
X X
X X
E X X
X X
X
:5.
22
2
2
9 5
2 34 5
6 2
2 9 5
4
− −
++ −
−
− ++ +
X
C XX
X
B X X
X
6.
7.
:
:
XX
X X
C XX
X
X X
X
−
− +
+× +
++
+
1
3 5 4
4 31
4 3
4 3
4
2
2
2
8. :
77 3
32
2 6
3
5 6
2
2
X
B XXX
X X
X X
A X
+
+× +
++
+ +
9.
10.
:
:
22
2
2
9 5
2 34 5
6 2
2 9 5
4
− −
++ −
−
− ++ +
X
C XX
X
B X X
X
6.
7.
:
:
XX
X X
C XX
X
X X
X
−
− +
+× +
++
+
1
3 5 4
4 31
4 3
4 3
4
2
2
2
8. :
77 3
32
2 6
3
5 6
2
2
X
B XXX
X X
X X
A X
+
+× +
++
+ +
9.
10.
:
: ++× −− −+
+ −
+× +
42
2 8
4
2 8
15
5
2
2
XX
X X
X X
C XX
11. :
XX
X X
X X
D XX
X
X X
++
+ +
−× −
− +−
5
6 5
36
6 18
3
2
2
2
12. :
X X
B
2 9 18− +13. : Multiplying the two first terms:
7X
: Multiplying the two firs
⋅ =X X
B
7 2
14. tt terms:
:
2 2 2X X X
B trinomial
⋅ =15.
Test 21Test 201. E X A
X B
BX AB
X AX
X A B
:
+× +
++
+ +
2
2 (( ) +
+( )+( ) +( )+( ) +(
X AB
B A B X
B X X
E X X
2.
3.
4.
:
:
:
1 2
3 5))+( ) +( )+( ) +( )+( ) +(
5.
6.
7.
B X X
B X X
C X X
:
:
:
6 6
2 10
3 8))+( ) +( )+( ) +( )+( ) +
8.
9.
10.
D X X
A X X
B X X
:
:
:
1 5
7 7
1 10(( )+
× +
++
+ +
11.
1
D A BA B
AB BA AB
A AB B
: 2
2
2 2
aLGeBra 1
test 21 - test 23
soLutions 341
E X A
X B
BX AB
X AX
X A B
:
+× +
++
+ +
2
2 (( ) +
+( )+( ) +( )+( ) +(
X AB
B A B X
B X X
E X X
2.
3.
4.
:
:
:
1 2
3 5))+( ) +( )+( ) +( )+( ) +(
5.
6.
7.
B X X
B X X
C X X
:
:
:
6 6
2 10
3 8))+( ) +( )+( ) +( )+( ) +
8.
9.
10.
D X X
A X X
B X X
:
:
:
1 5
7 7
1 10(( )+
× +
++
+ +
11.
1
D A BA B
AB BA AB
A AB B
: 2
2
2 22
22. E X BYX BY
BYX BY
X BYX
:
+× +
+ ( )+
2
2
:
:
X BYX BY
C X R X T
B X R X R
2 22+ + ( )
+( ) +( )+( ) +( )
13.
14.
115. B factors:
Test 221.
2.
3.
4.
B: 2X A X A
2AX A
2X AX
2X 3AX A
final term is A
E: 3AX
B: 2X 1 X 2
E: 3X 2 X 4
2
2
2 2
2
( )( )( )
( )
+× +
+
+
+ +
+ ++ +
Test 22
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
D: 2X 3 X 3
A: 4X 6 X 1
B: 2X 1 X 1
A: 3A 4 A 2
E: 2Y 6 Y 3
E: 5B 2 B 2
D: 2A B A B
2AB B
2A AB
2A 3AB B
B: A C 2A B BA BC
2A 2CA
2A 2C B A BC
A: 3X R X R
E: 2A B A 3B
D: 5X Y X Y
5XY Y
5X XY
5X 6XY Y
first and second term are
affected by the coefficient "5"
2
2
2 2
2
2
2
2
2 2
( ) ( )( )
( )( ) ( )( )
( )( )
( )
( )( )( )
( )
( )
( )( )
+ ++ ++ ++ ++ ++ +
+× +
++
+ +
+× +
++
+ + +
+ ++ +
+× +
++
+ +
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
D: 2X 3 X 3
A: 4X 6 X 1
B: 2X 1 X 1
A: 3A 4 A 2
E: 2Y 6 Y 3
E: 5B 2 B 2
D: 2A B A B
2AB B
2A AB
2A 3AB B
B: A C 2A B BA BC
2A 2CA
2A 2C B A BC
A: 3X R X R
E: 2A B A 3B
D: 5X Y X Y
5XY Y
5X XY
5X 6XY Y
first and second term are
affected by the coefficient "5"
2
2
2 2
2
2
2
2
2 2
( ) ( )( )
( )( ) ( )( )
( )( )
( )
( )( )( )
( )
( )
( )( )
+ ++ ++ ++ ++ ++ +
+× +
++
+ +
+× +
++
+ + +
+ ++ +
+× +
++
+ +
Test 231.
2.
3.
4.
5.
C: the last term
D: X A X B
BX AB
X AX
X A B X AB
first negative, second positive
A: X 2X 3
3X 6
X 2X
X 5X 6
D: X 2X 3
3X 6
X 2X
X X 6
C: X 2X 3
3X 6
X 2X
X X 6
2
2
2
2
2
2
2
2
( )
−× −− +−
− + +
−× −− +−
− +
−× +
−−
+ −
+× −− −+
− −
Test 23
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
B: X 1 X 2
E: X 4 X 1
B: X 3 X 2
A: A 3 A 4
B: A 3 A 4
E: X Y X Y
XY Y
X XY
X 2XY Y
D: X Y X Y
XY Y
X XY
X Y
D: X R X R
E: they are either both
negative or both positive
D: the second term of either
factor with the largest value
2
2
2 2
2
2
2 2
( )( )( )
( )( )( )( )
( )( )( )
( )( )
− +− +− −+ −− +
−× −− +
−
− +
+× −
− −+
−
− −
aLGeBra 1
test 23 - unit test i i
soLutions342
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
B: X 1 X 2
E: X 4 X 1
B: X 3 X 2
A: A 3 A 4
B: A 3 A 4
E: X Y X Y
XY Y
X XY
X 2XY Y
D: X Y X Y
XY Y
X XY
X Y
D: X R X R
E: they are either both
negative or both positive
D: the second term of either
factor with the largest value
2
2
2 2
2
2
2 2
( )( )( )
( )( )( )( )
( )( )( )
( )( )
− +− +− −+ −− +
−× −− +
−
− +
+× −
− −+
−
− −
Unit Test II
1.
2.
3.
4.
5.
5 5 5 5 or 3,125
3 3 3 3 27
2 2 2 or 116
3 ÷3 3 3 or 6,561
A B AB A B A B
2 3 2 3 5
3
22
2 2 4
10 2 10 2 8
2 3 4 2 1 3 4 3 7
( )( ) ( ) ( ) ( )
⋅ = =
− = − − − = −
= =
= =
= =
( )( )
+
− − −
−
+ +
Unit Test III
6.
1.
1.
3X 2X 1
3X 2
3X 2X
3X X 2
.05N .10D 1.10 100
N D 16 5
5N 10D 1105N 5D 80
5D 30D 6
using elimination:
2X Y 1 2 4X 2Y 22Y 6
4X 4
X 1
2Y 6 Y 3
1, 3
using substitution:
2Y 6 Y 3
2X 1 Y 2X 1 3
2X 2X 1
1, 3
using graphing: 1, 3
2
2
( )
( )( )
( ) ( )( ) ( )
( )
( )( )
+× −− −+
− −
+ = =>+ = − =>
+ =− − = −
==
− = − => − = −===
= => =
= => =
+ = => + ===
II
III
6.
1.
1.
3X 2X 1
3X 2
3X 2X
3X X 2
.05N .10D 1.10 100
N D 16 5
5N 10D 1105N 5D 80
5D 30D 6
using elimination:
2X Y 1 2 4X 2Y 22Y 6
4X 4
X 1
2Y 6 Y 3
1, 3
using substitution:
2Y 6 Y 3
2X 1 Y 2X 1 3
2X 2X 1
1, 3
using graphing: 1, 3
( )
( )( )
( ) ( )( ) ( )
( )
( )( )
+× −− −+
− −
+ = =>+ = − =>
+ =− − = −
==
− = − => − = −===
= => =
= => =
+ = => + ===
II
III
Y
X
2. using elimination:
Y 3 X 2X 3 2 Y
X 5 Y
X 5 Y 2 2X 10 2Y2X 1 Y
11 YY 11
2X 1 Y 2X 1 112X 12X 6
6, 11
using substitution:
2X 1 Y
Y 3 X 2 2X 1 3 X 2
2X 4 X 22X X 2 4
X 6
2X 1 Y 2 6 1 Y
12 1 Y11 Y
using graphing: We can only estimate,
but 6, 11 looks reasonable.
( )
( )
( )
( )
( )
( )
− = +− − − = −
− − = −
− − = − => − − = −− =− = −
=
− = => − ===
− =
− = + => − − = +− = +− = +
=
− = => − =− =
=
aLGeBra 1
unit test i i - test 24
soLutions 343
using elimination:
Y 3 X 2X 3 2 Y
X 5 Y
X 5 Y 2 2X 10 2Y2X 1 Y
11 YY 11
2X 1 Y 2X 1 112X 12X 6
6, 11
using substitution:
2X 1 Y
Y 3 X 2 2X 1 3 X 2
2X 4 X 22X X 2 4
X 6
2X 1 Y 2 6 1 Y
12 1 Y11 Y
using graphing: We can only estimate,
but 6, 11 looks reasonable.
( )
( )
( )
( )
− = +− − − = −
− − = −
− − = − => − − = −− =− = −
=
− = => − ===
− =
− = + => − − = +− = +− = +
=
− = => − =− =
=
Y
X
1. 2N 1 N 42N N 4 1
N 3
3, 5, 7
+ = +− = −
=
IV
1.
2.
3.
2X 28 2 X 14
2X 8X 6 2 X 4X 3
2 X 3 X 1
3X 19X 20 3X 4 X 5
2Y ≤ 4X 8
Y 2X 4
2 0 ≤ 4 0 8
0 ≤ 8 false
2 3 ≤ 4 4 8
– 6 ≤ 8 true
2 2
2 2
2
( )( )
( )( ) ( )
( ) ( )
( )
( )( ) ( )
( )
+ = +
+ + = + += + +
+ + = + +
−= −
−−
− −
V
VI
2X 28 2 X 14
2X 8X 6 2 X 4X 3
2 X 3 X 1
3X 19X 20 3X 4 X 5
2Y ≤ 4X 8
Y 2X 4
2 0 ≤ 4 0 8
0 ≤ 8 false
2 3 ≤ 4 4 8
– 6 ≤ 8 true
( )( ) ( )
( ) ( )
( ) ( )
+ = +
+ + = + += + +
+ + = + +
−= −
−−
− −
V
VI
Y
X
Test 241.
2.
3.
4.
5.
6.
7.
A: X 3
E: X 4
B: X 1
C: X 6
B: X 2
E: X 5
A: X 1
X 2 X 3X 2
X 2X
X 2
X 2
2
2( )
( )
++++++
+
+ + +
− ++
− +
Test 24
8.
9.
10.
11.
12.
13.
14.
D: X 6 r 2
X 3 X 9X 20
X 3X
6X 20
6X 18
2
E: X r 5
X 4 X 4X 5
X 4X
5
B : X 7
X 3 X 4X 21
X 3X
7X 21
7X 21
C: X 3
X 5 X 8X 15
X 5X
3X 15
3X 15
B: X 4 r 2
X 2 X 6X 10
X 2X
4X 10
4X 8
2
A: X 5
X 5
5X 25
X 5X
X 10X 25
D: X 7X 7
7X 49
X 7X
X 14X 49
2
2
2
2
2
2
2
2
2
2
2
2
2
2
( )
( )
( )
( )
( )
( )
( )
( )
+
+ + +
− ++
− +
−
+ + −
− +
−
−
+ − −
− +− −
− − −
+
+ + +− +
+
− +
+
+ + +
− ++
− +
+× +
++
+ +
+× +
++
+ +
aLGeBra 1
test 24 - test 26
soLutions344
8.
9.
10.
11.
12.
13.
14.
D: X 6 r 2
X 3 X 9X 20
X 3X
6X 20
6X 18
2
E: X r 5
X 4 X 4X 5
X 4X
5
B : X 7
X 3 X 4X 21
X 3X
7X 21
7X 21
C: X 3
X 5 X 8X 15
X 5X
3X 15
3X 15
B: X 4 r 2
X 2 X 6X 10
X 2X
4X 10
4X 8
2
A: X 5
X 5
5X 25
X 5X
X 10X 25
D: X 7X 7
7X 49
X 7X
X 14X 49
2
2
2
2
2
2
2
2
2
2
2
2
2
2
( )
( )
( )
( )
( )
( )
( )
( )
+
+ + +
− ++
− +
−
+ + −
− +
−
−
+ − −
− +− −
− − −
+
+ + +− +
+
− +
+
+ + +
− ++
− +
+× +
++
+ +
+× +
++
+ +
15. B: 2X 7 X 5
10X 35
2X 7X
2X 17X 35
2
2
+× +
++
+ +
Test 251.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
E: X B X B
BX B
X BX
X B
C: R 4 R 4
D: S 5 S 5
A: R T R T
RT T
R RT
R T
A: X 6 X 6
E: none of the above
E: none of the above
C: X 10 X 10
C: X 8 X 88X 64
X 8X
X 64
A: X 3 X 3
3X 9
X 3X
X 9
D: X 7 X 77X 49
X 7X
X 49
2
2
2 2
2
2
2 2
2
2
2
2
2
2
( ) ( )
( ) ( )
( ) ( )
( )( )
+× −
− −+
−+ −+ −
+× −
− −+
−− +
+ −
+× −− −+
−
+× −− −+
−
+× −− −+
−
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
E: X B X B
BX B
X BX
X B
C: R 4 R 4
D: S 5 S 5
A: R T R T
RT T
R RT
R T
A: X 6 X 6
E: none of the above
E: none of the above
C: X 10 X 10
C: X 8 X 88X 64
X 8X
X 64
A: X 3 X 3
3X 9
X 3X
X 9
D: X 7 X 77X 49
X 7X
X 49
2
2
2 2
2
2
2 2
2
2
2
2
2
2
( ) ( )
( ) ( )
( ) ( )
( )( )
+× −
− −+
−+ −+ −
+× −
− −+
−− +
+ −
+× −− −+
−
+× −− −+
−
+× −− −+
−12.
13.
14.
15.
C: add to 10
A: be the same
B: 4 5 205 5 25
2,025
D: 6 7 423 7 21
4,221
× =× =
× =× =
Test 261.
2.
3.
4.
5.
6.
D: X 81 X 9 X 9
X 9 X 3 X 3
D: X 9 X 3 X 3
E: A 16 A 4 A 4
A 4 A 2 A 2
D: 4X
B: 5X
E: 1,000 is not a perfect square
4 2 2
2
4 2 2
4 2 2
2
4
( )( )( )
( )( )( )( )( )
( ) ( )
( )( )
− = + −
= + − +
− = + −
− = + −
= + + −
Test 26
aLGeBra 1
test 26 - test 27
soLutions 345
1.
2.
3.
4.
5.
6.
D: X 81 X 9 X 9
X 9 X 3 X 3
D: X 9 X 3 X 3
E: A 16 A 4 A 4
A 4 A 2 A 2
D: 4X
B: 5X
E: 1,000 is not a perfect square
4 2 2
2
4 2 2
4 2 2
2
4
( )( )( )
( )( )( )( )( )
( ) ( )
( )( )
− = + −
= + − +
− = + −
− = + −
= + + −
7.
8.
9.
10.
11.
12.
13.
14.
15.
D: B 10,000 B 100 B 100
B 100 B 10 B 10
C: X Y X Y X Y
B: X Y X Y X Y
X Y X Y X Y
D: 2X 16X 24X 2X X 8X 12
2X X 2 X 6
E: 4X 64X 4X X 16
4X X 4 X 4
A: 3X 12X 15X 3X X 4X 5
3X X 5 X 1
C: 8X 72X 8X X 9
8X X 3 X 3
B: 480 ÷ 60 8 hours
D: 5 65 325 miles
4 2 2
2
4 4 2 2 2 2
4 4 2 2 2 2
2 2
3 2 2
3 2
3 2 2
3 2
( )( )( )
( )
( )
( )
( )
( )( )( )( )( )
( ) ( )
( )
( )( ) ( )
( )( ) ( ) ( )
( )( )
( )( )( )
( )( )( )( )
( )
− = + −
= + + −
− = + −
− = + −
= + + −
+ + = + += + +
− = −= + −
− − = − −= − +
− = −= + −
=× =
Test 271.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
C: subtract 2 from each side
E: Each value of X must make at least
one term equal 0.
A: divide each term by 2
B: factor out X
A: Each value of X must make
at least one term equal 0.
C: X 11X 30 0
X 5 X 6 0
X 5 or X 6
A: 2X 7X 6 0
2X 3 X 2 0
2X 3 02X 3
X 32
X 2 0X 2
E: 2X 7X 6 0
2X 3 X 2 0
2X 3 02X 3
X 32
X 2 0X 2
B: X 9X 20 0
X 4 X 5 0
X 4 0X 4
X 5 0X 5
D: 3X 3X 18 0
3 X X 6 0
3 X 3 X 2 0
X 3 0X 3
X 2 0X 2
C: X 8X 16 1
X 8X 15 0
X 3 X 5 0
X 3 0X 3
X 5 0X 5
2
2
2
2
2
2
2
2
( ) ( )
( )
( )
( )
( )( ) ( )
( ) ( )
( )
( )
( )
( )
+ + =+ + =
= − = −
+ + =+ + =
+ == −
= −
+ == −
− + =− − =
− ==
=
− ==
+ + =+ + =
+ == −
+ == −
− − =
− − =− + =
− ==
+ == −
− + =− + =
− − =
− ==
− ==
Test 27
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
C: subtract 2 from each side
E: Each value of X must make at least
one term equal 0.
A: divide each term by 2
B: factor out X
A: Each value of X must make
at least one term equal 0.
C: X 11X 30 0
X 5 X 6 0
X 5 or X 6
A: 2X 7X 6 0
2X 3 X 2 0
2X 3 02X 3
X 32
X 2 0X 2
E: 2X 7X 6 0
2X 3 X 2 0
2X 3 02X 3
X 32
X 2 0X 2
B: X 9X 20 0
X 4 X 5 0
X 4 0X 4
X 5 0X 5
D: 3X 3X 18 0
3 X X 6 0
3 X 3 X 2 0
X 3 0X 3
X 2 0X 2
C: X 8X 16 1
X 8X 15 0
X 3 X 5 0
X 3 0X 3
X 5 0X 5
2
2
2
2
2
2
2
2
( )
( ) ( )
( )
( )
( )
( )( ) ( )
( ) ( )
( )
( )
( )
( )
+ + =+ + =
= − = −
+ + =+ + =
+ == −
= −
+ == −
− + =− − =
− ==
=
− ==
+ + =+ + =
+ == −
+ == −
− − =
− − =− + =
− ==
+ == −
− + =− + =
− − =
− ==
− ==
12.
13.
14.
15.
E: 2X 2X 4 20
2X 2X 24 0
2 X X 12 0
X 4 X 3 0
X 4 0X 4
X 3 0X 3
D: 3X 9X 12
3X 9X 12 0
3 X 3X 4 0
X 4 X 1 0
X 4 0X 4
X 1 0X 1
B: X 10X 25 0
X 5 X 5 0
X 5 0X 5
A: X R S X RS 0
X R X S 0
X R 0X R
X S 0X S
2
2
2
2
2
2
2
2
( )
( )( )
( )
( ) ( )
( )( )
( )( )
( )( )
( )
− − =− − =
− − =− + =
− ==
+ == −
+ =+ − =
+ − =+ − =
+ == −
− ==
− + =− − =
− ==
+ + + =+ + =
+ == −
+ == −
aLGeBra 1
test 28 - test 30
soLutions346
Test 281.
2.
3.
4.
5.
B: 12 inches 1 foot
feet in denominator to cancel
inches in numerator to remain in answer
D: 4 quarts 1 gallon
quarts in denominator
gallons in numerator
C: 3 feet 1 yard
feet in denominator
yards in numerator
A: 16 ounces 1 pound
pounds in denominator
ounces in numerator
D: 2,000 pounds 1 ton
pounds in denominator
tons in numerator
=
=
=
=
=
Test 28
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
B: 2 pints 1 quart
pints in denominator
quarts in numerator
B: 48 in1
1 ft12 in
4 ft
C: 16 gal
14 qt1gal
64 qt
A: 10 lb1
16oz1lb
160 oz
D: 6 qt
12 pt1qt
12 pt
B: 8,000 lb1
1 ton2,000 lb
4 tons
C: 80 oz1
1 lb16 oz
5 lb
D: 6 yd
136 in1yd
216 in
C: the name of the desired answer
E: equal to 1
=
× =
× =
× =
× =
× =
× =
× =
Test 291.
2.
3.
4.
5.
6.
7.
8.
B: 2
C: 3
C: 12 inches 1 foot
5,280 feet 1 mile
B: 1 quart 2 pints
1 gallon 4 quarts
E: 2 yd
13 ft1yd
3 ft1yd
18 ft
D: 6 yd
13 ft1yd
3 ft1yd
3 ft1yd
162 ft
C: 8 yd
13 ft1yd
3 ft1yd
72 ft
72 ft1
12 in1ft
12 in1ft
10,368 in
B: 87,120 ft1
1 acre
43,560 ft
87,120 acres43,560
2 acres
22
23
22
22
2
2
===
=
× × =
× × × =
× × =
× × =
× =
=
1.
2.
3.
4.
5.
6.
7.
8.
B: 2
C: 3
C: 12 inches 1 foot
5,280 feet 1 mile
B: 1 quart 2 pints
1 gallon 4 quarts
E: 2 yd
13 ft1yd
3 ft1yd
18 ft
D: 6 yd
13 ft1yd
3 ft1yd
3 ft1yd
162 ft
C: 8 yd
13 ft1yd
3 ft1yd
72 ft
72 ft1
12 in1ft
12 in1ft
10,368 in
B: 87,120 ft1
1 acre
43,560 ft
87,120 acres43,560
2 acres
22
23
22
22
2
2
===
=
× × =
× × × =
× × =
× × =
× =
=
9.
10.
11.
12.
13.
14.
15.
C: 4 ft 4 ft 16 ft 256 ft
256 ft1
1 cord
128 ft
256 cords128
2 cords
E: 6 m1
100 cm1m
100 cm1m
100 cm1m
6,000,000 cm
B: 1yd
13 ft1yd
3 ft1yd
9 ft
3 ft 9 ft
C: 9 ft 9 ft
A: 1mi1
5,280 ft1mi
5,280 ft1mi
27,878,400 ft
27,878,400 ft 43,560 ft
D: Cannot be determined, because we don't
know the relationship between Xand Y.
B: 8 yd
13 ft1yd
3 ft1yd
3 ft1yd
216 ft
215 ft 216 ft
3
3
3
3
3
22
2 2
2 2
22
2 2
33
3 3
× × =
× = =
× × × =
× × =
<
=
× × =
>
× × × =
<
Test 301.
2.
3.
4.
5.
6.
7.
8.
9.
D: 5 km1
.62 mi1 km
3.1 mi
B: 6 kg
12.2 lb1kg
13.2 lb
A: 3 yd
1.9 m1yd
2.7 m
B: 6 mi1
1.6 km1 mi
9.6 km
D: 8 lb1
.45 kg1lb
3.6 kg
E: 6 m1
1.1 yd1m
6.6 yd
A: 9 cm1
.4 in1cm
3.6 in
C: 9 in1
2.5 cm1in
22.5 cm
E: 3 liters1
1.06 qt1liters
3.18 qt
× =
× =
× =
× =
× =
× =
× =
× =
× =
Test 30
aLGeBra 1
test 30 - test 32
soLutions 347
1.
2.
3.
4.
5.
6.
7.
8.
9.
D: 5 km1
.62 mi1 km
3.1 mi
B: 6 kg
12.2 lb1kg
13.2 lb
A: 3 yd
1.9 m1yd
2.7 m
B: 6 mi1
1.6 km1 mi
9.6 km
D: 8 lb1
.45 kg1lb
3.6 kg
E: 6 m1
1.1 yd1m
6.6 yd
A: 9 cm1
.4 in1cm
3.6 in
C: 9 in1
2.5 cm1in
22.5 cm
E: 3 liters1
1.06 qt1liters
3.18 qt
× =
× =
× =
× =
× =
× =
× =
× =
× =
Test 30
10.
11.
12.
13.
14.
15.
B: 1gal
14 qt
1gal.95 liters
1qt3.8 liters
B: 2 qt
1.95 liters
1qt1.9 liters
1.9 liters 2liters
A: 5 mi1
1.6 km1mi
8 km
8 km 5 km
B: X lb1
1 kg2.2 lb
X kg2.2
12.2
X kg .45X kg
.45X kg 1X kg
C: 2 oz1
28 g1oz
56 g
56 g 56 g
D: Cannot be determined from the
information given: The relationship between
centimeters and inches is known, but the
relationship between X and Y is not known.
× × =
× =
<
× =
>
× =
= =
<
× =
=
Test 311.
2.
3.
4.
5.
6.
7.
8.
9.
B: radical
A: add the exponents
C: 27 27 3
E: X X X X
B: 125 125 5 25
A: X X
D: 2 16 2 16 2 2 4
B: Y Y Y Y Y
D: X X X
X X X
13 3
313
3 13 1
23 3 2
2
23 3 2
14 4
16
25
16
25
530
1230
1730
2 412 2 4
12
612
6 12 3
( )( )
( )
( ) ( )
( )
= =
= = =
= = =
=
⋅ = ⋅ = ⋅ =
= = =
⋅ =
= = =
( )
+ +
+
1.
2.
3.
4.
5.
6.
7.
8.
9.
B: radical
A: add the exponents
C: 27 27 3
E: X X X X
B: 125 125 5 25
A: X X
D: 2 16 2 16 2 2 4
B: Y Y Y Y Y
D: X X X
X X X
13 3
313
3 13 1
23 3 2
2
23 3 2
14 4
16
25
16
25
530
1230
1730
2 412 2 4
12
612
6 12 3
( )( )
( )
( ) ( )
( )
= =
= = =
= = =
=
⋅ = ⋅ = ⋅ =
= = =
⋅ =
= = =
( )
( )
+ +
+
10.
11.
12.
13.
14.
15.
C: 10 1,000 10 10
10 10 10
A: 2 2 2 4
2 2 2 2
4 2
B: X X X X X X
X X
C: 3 3 3 3
9 3 3
3 3
C: 10 1,000 10 10
10 10
10 10
A: B B B
B
B B
B B
23
23 3
23
3 23
93
113
2
12
212
2 1
3 313
3 3 13
6 13
193
193 19
13
313
3 1
2 2 3
2 3 5
5 5
3 512
2
3 512
2
812
2
8 12
2 8
8 4
( )
( )
( ) ( )
( )
⋅ = ⋅
= = =
= × =
= = =>
= = =
<
= = =
= ==
⋅ = ⋅ =
==
=
=
= =
>
( )
( )
( )
( )
+ +
+ + +
+
+
Test 321.
2.
3.
4.
5.
6.
7.
8.
9.
10.
A: To simplify computations with very large
or very small numbers
B: 6,300,000 6.3 10
D: 543,000 5.43 10
B: .00065 6.5 10
E: .0000781 7.81 10
C: 10 10 10 10
C: 10 10 10 10
A: 12,000 .006 1.2 10 6 10
C: 3.6 10 .0000036
E: 1.02 10 102,000
6
5
4
5
7 7 7 7 14
1 6 1 6 5
4 3
6
5
( )( )( )( )
( ) ( )
= ×
= ×
= ×
= ×
= =
= =
× = × ×
× =
× =
( )
−
−
+
− + − −
−
−
aLGeBra 1
test 32 - test 33
soLutions348
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
A: To simplify computations with very large
or very small numbers
B: 6,300,000 6.3 10
D: 543,000 5.43 10
B: .00065 6.5 10
E: .0000781 7.81 10
C: 10 10 10 10
C: 10 10 10 10
A: 12,000 .006 1.2 10 6 10
C: 3.6 10 .0000036
E: 1.02 10 102,000
6
5
4
5
7 7 7 7 14
1 6 1 6 5
4 3
6
5
( )( )( )( )
( ) ( )
= ×
= ×
= ×
= ×
= =
= =
× = × ×
× =
× =
( )
−
−
+
− + − −
−
−
11.
12.
13.
14.
15.
C: .25 130,000 2.5 10 1.3 10
2.5 1.3 10 10
3.25 10
D: 50,000,000 .610 5 10 6.1 10
5 6.1 10 10
30.5 10
3.05 10
C: 2.4 3.06 7.344 ≈ 7.3 2 SD
D: 1.24 10 4.7 10
1.24 4.7 10 10
5.828 10
≈ 5.8 10 2 SD
B: 6.25 10 ÷ 3.241 10
6.25÷3.241 10 ÷10
1.9284 10 rounded
≈ 1.93 10 3 SD
1 5
1 5
4
7 1
7 1
6
7
6 3
6 3
9
9
8 4
8 4
4
4
( )( )( )
( )( )( )
( )( )( )
( ) ( )( )
( )
( )
( )
( )
( )
( )
( )
( )
× = × ×
= × ×
= ×
× = × ×
= × ×
= ×= ×
× =
× ×
= × ×
= ××
× ×
=
= ×
×
−
−
−
−
Test 331.
2.
3.
4.
5.
6.
7.
8.
C: 10
C: 10
C: Write the number in exponential notation
E: 4
D: 10
C: 5 125, and is the largest power
of 5 less than 300.
A: 4 64, and is the largest power
of 4 less than 95.
C: 4 is the largest power of 4 less than 34.
4 16; 4 4; 4 1
2
16 34 32
2
0
4 2 0
2
2
1 2 2
0
2 4 0 4 2 4 202
10
43
3
2
2 1 0
2 1 04
=
=
= = =
× + × + × =
1.
2.
3.
4.
5.
6.
7.
8.
C: 10
C: 10
C: Write the number in exponential notation
E: 4
D: 10
C: 5 125, and is the largest power
of 5 less than 300.
A: 4 64, and is the largest power
of 4 less than 95.
C: 4 is the largest power of 4 less than 34.
4 16; 4 4; 4 1
2
16 34 32
2
0
4 2 0
2
2
1 2 2
0
2 4 0 4 2 4 202
10
43
3
2
2 1 0
2 1 04
=
=
= = =
× + × + × =
9.
10.
11.
12.
13.
14.
15.
E: 2 is the largest power of 2 less than 45.
2 32; 2 16; 2 8; 2 4; 2 2; 2 1
1
32 45 32
13
0
16 13 0
13
1
8 13 8
5
1
4 5 4
1
0
2 1 0
1
1
1 1 1
0
1 2 0 2 1 2 1 2 0 2 1 2 101101
B: 12 is the largest power of 12 less than 356.
12 144; 12 12; 12 1
2
144 356 288
68
5
12 68 60
8
8
1 8 8
0
2 12 5 12 8 12 258
E: 122 1 6 2 6 2 6
1 36 2 6 2 1 36 12 2 50
B: 4B3 4 12 11 12 3 12
4 144 1112 3 1
576 132 3 711
A: 52A 5 12 2 12 10 12
5 144 2 12 10 1
720 24 10 754
E: 122 1 3 2 3 2 3
1 9 2 3 2 1 9 6 2 17
B: 1000 1 7 0 7 0 7 0 7
1 343 0 49 0 7 0 1 343
5
5 4 3 2 1 0
5 4 3 2 1 02
2
2 1 0
2 1 012
62 1 0
10
122 1 0
10
122 1 0
10
32 1 0
10
73 2 1 0
10
( ) ( )
( ) ( )
( ) ( )
( )
( ) ( ) ( )
( ) ( ) ( )
( )
( ) ( )
= = = = = =
× + × + × + × + × + × =
= = =
× + × + × =
= × + × + ×
= + + = + + =
= × + × + ×
= + += + + =
= × + × + ×
= + += + + =
= × + × + ×
= + + = + + =
= × + × + × + ×
= + + + =
aLGeBra 1
test 34 - unit test i i i
soLutions 349
Test 341.
2.
3.
4.
5.
6.
7.
A: circle
C: ellipse
B: the coordinates of the center of a circle
C: P is the radius of a circle
E: Only ellipse has different X
and Y coefficients
C: 0, 0
A: radius 9 3
( )= =
8.
9.
E
D
:
: center at
− −( ) = − −( ) = ( )−
3 3 4 4 3 4
3
; : ,
,, ;
, ;
−( ) = =
( )3 4 2
3 2
radius
A radi10. : center at uus
E enter at radius
not o
= =
−( ) = =
1 1
3 3 1 111. : c , ;
nn graph
D enter at radius
C
, ;12.
13.
: c 3 3 2 4−( ) = =
::
When X is 0:
center at
X Y
Y
,0 0
4 4
0 4
2 2
2 2
( )+ =
( ) + ==
=== ±
+ =
+ ( ) =
4
4 4
11
4 4
4 0 4
2
2
2
2 2
Y
YY
Y
X
X
When Y is 0: X2
22 42
0 1 2 0 2 0
== ±
( ) −( ) −( ) (X
Points: 0, 1 ; , ; , ; , ))( )
+ =
(
14. E center at
Y
:
When X is 0: 4X
4 0
2
,0 0
42
)) + =
== ±
+ =
+ ( ) =
2 2
2
2
2 2
4
42
4
4 0 4
4
Y
YY
Y
X
When Y is 0: 4X2
XX
XX
2
2
4
11
0 2 0 2 1 0
=== ±
( ) −( ) ( ) −Points: , ; , ; , ; 11 0
0 0
,
, ;
( )
( )not on graph
: 15. C center at radiuus = =1 1
Test 351.
2.
3.
4.
5
C ellipse
E hyperbola
B circle
A line
:
:
:
:
..
6.
D parabola
B I
:
: and III
When a pair of factorrs multiply to equal a
positive number, they wiill always be both
positive or both negative.
7.. C II
When
: and IV
a pair of factors multiply too equal a
negative number, one will be positivee,
and the negative.
: The parabola g
othter
D8. eets narrower.
: 9.
10.
A XY Y
Y
E
= => −( ) =
=−
= −
12 4 12124
3
::
chart and use test points
:
hyperbola
make
D11. hyperbola
chart and use test points
:
make
B12. hhyperbola
chart and use test points
:
make
A p13. aarabola
make
C par
chart and use test points
: 14. aabola
make
B parab
chart and use test points
: 15. oola
make chart and use test points
Unit Test IIIUnit Test IIII
1. 2 1
2 2 5 2
2 4
2
2
2
X
X X X
X X
X
+
+ + +
− +( )+
−− +( )
+× +
+++ +
X
XXX
X X
X X2
2 12
4 2
2
2 5 2
2
2
aLGeBra 1
unit test i i i - unit test i i i
soLutions350
2. X X
X X X X
X X
X X
X X
2
3 2
3 2
2
2
5 1
2 3 9 2
2
5 9
5 10
+ +
− + − −
− −( )−
− −(( )−−
+ +× −
− − −+ +
XX
X XX
X X
X X X
22
5 12
2 10 2
5
2
2
3 2
X X X
X X
X X
3 2
2 2
3 9 2
3 12 3 4
3 2 2
+ − −
− = ( ) −( )= ( ) −( ) +
II1.
(( )− = −( ) +( )− − = ( ) − −( )
=
2.
3.
Q R Q R Q R
X X X X
2 2
2 22 4 30 2 2 15
22 3 5
5 16 10
5 6 0
2 3
2
2
( ) +( ) −( )
+ + =+ + =
+( ) +
X X
X X
X X
X X
III1.
(( ) =+ =
= −+ =
= −
+ + =
−( ) + −( ) +
0
2 02
3 03
5 16 10
2 5 2 1
2
2
XX
XX
X X
66 104 10 16 10
10 10
5 16 10
3 5 3 16 1
2
2
=− + =
=
+ + =
−( ) + −( ) + =
X X
00
9 15 16 1010 10
− + ==
2. 2 18 0
2 9 0
2 3 3 0
2 00
3
2
X X
X X
X X X
XX
X
− =( ) −( ) =
( ) −( ) +( ) ===
−− ==
+ == −
− =
( ) − ( ) =− =
=
3 03
3 03
2 18 0
2 0 18 0 0
0 0 00 0
3
3
XX
X
X X 22 18 0
2 3 18 3 0
2 27 54 054 54 0
0 0
2
3
3
3
X X
X
− =
( ) − ( ) =( ) − =
− ==
−118 0
2 3 18 3 0
2 27 54 054 54 0
0 0
3
X =
−( ) − −( ) =−( ) + =− + =
=IV
1. 11001
281
2 800
61
621
3 72
oz goz
g
km mikm
mi
× =
× =
,
. .2.
VV
VI
1.
2.
1.
456 700 000 4 567 10
0260 2 6 10
0
8
2
, , .
. .
.
= ×
= × −
0003 4 2 3 10 4 2 10
3 4 2 10 10
12
4 0
4 0
× = ×( ) ×( )= ×( ) ×( )=
−
−
. .
.
..
.
6 10
1 26 10 1 10
4
3 3
×= × ×
−
− −or
with significant diggits taken
into account: either answer
is accepptable.
2. 6 800 000200 000
6 8 10 2 10
6
6 5, ,,
.
.
= ×( ) ×( )
=
÷
88 2 10 10
3 4 10 3 10
6 5
1 1
÷ ÷( )( )= × ×. or
with significantt digits taken
into account: either answer
is aacceptable.
aLGeBra 1
unit test i i i - FinaL eXaM
soLutions 351
VII
VIII
1.
2.
3.
1.
196 14
100 10
18 81 9
7
2
2
2
=
=
+ + = +
A A
X X X
iss the largest power of 7 < 70
72 = = =49 7 7 7 11 0; ;
11
49 7049
21
3
7 2121
0
0
1 00
0
1 7 3 7 0 7 130
2
2 1 07× + × + × =
2. 2210 2 3 2 3 1 3 0 3
2 27 2 9 1 3 0 1
33 2 1 0= × + × + × + ×
= ( ) + ( ) + ( ) + ( )= 554 18 3 0 75
16 16 4
1 000 1 000
10
12
23 3 2
+ + + =
= =
( ) =
IX
1.
2. , , == =10 1002
X1. hyperbola
X Y
3 13
3 13
13
3
13
3
2 12
2 12
12
2
12
2
1
−
−
−
−
−
−
−
−
−−−
11 1
Y
X
2. circle: center at 0, 0( )= =
;
radius 4 2
Y
X
Final ExamI
1. − + ( ) − = + −
= −
= −
= − =
12
3 14
1 9
14
8
14
324
314
20 2ab
−−
=
( ) ( ) = ⋅ = ⋅ =− = −
7 34
16 4
2 2 4 4 64 4 256
6 8 2
2
23
2 3
2.
3.
4.
X X
==
+ + = +
=
+ = +− −
2
4 4 2
81 9
3 5 3 5
2
12
2
4 12 4
5.
6.
7.
X X X
X
X
X
XX X XXX X X
X X X X
= +
− = ( ) −( ) = ( ) −( ) +( )
3 5
3 27 3 9 3 3 3
5
6 2
2 2
II1.
2. XX X X X
X X X X X X
X
2
3 2 2
9 2 5 1 2
5 6 5 6
− − = +( ) −( )
+ + = ( ) + +( )= (
3.)) +( ) +( )
− − = ( ) − −( )= ( ) +( )
X X
Y Y Y Y
Y
2 3
14 7 42 7 2 6
7 2 3
2 24.
YY −( )2
III.
IV.
1.
1.
10 10
10 102
3
6 3
3 2 3
2
=
==
−
( )( )( )( ) ( )( )
X
X
X
X 66 0
3 2 0
3 00
2 02
16
12
23
30 1
X
X X
XX
XX
X
=( ) −( ) =
==
− ==
− =
( )
2.
6630 1
230 2
3
306
302
603
− ( )
= ( )
− =
aLGeBra 1
FinaL eXaM - FinaL eXaM
soLutions352
III.
IV.
1.
1.
10 10
10 102
3
6 3
3 2 3
2
=
==
−
( )( )( )( ) ( )( )
X
X
X
X 66 0
3 2 0
3 00
2 02
16
12
23
30 1
X
X X
XX
XX
X
=( ) −( ) =
==
− ==
− =
( )
2.
6630 1
230 2
3
306
302
603
− ( )
= ( )
− =
X
X
55 15 205 35
7
25 4
100 25 4
100
XXX
X X
X X
− ===
+ =( ) + =
3. . .
( . . )
XX XX
X
+ ==
= =
25 40125 40
40125
825
or .32
V.
1. parabola
graph
X Y
see
0 01 21 22 82 8
−
−
Y
X
2. ellipse
X Y
Y
YY
When X =+ =
( ) + =
== ±
0
4 16
4 0 16
164
2 2
2 2
2
: WWhen Y
Poi
=+ =
+ ( ) =
=== ±
0
4 16
4 0 16
4 16
42
2 2
2 2
2
2
:
X Y
X
X
XX
nnts:
see grap
0 4 0 4 2 0 2 0, ; , ; , ; ,( ) −( ) +( ) −( )hh
Y
X
3. y slope− = =intercept
see graph
1 3;
Y
X
