SELF CHECK!

Make sure you are prepared for this test!

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m = —11

m = —-2 3 ( 3, 4 )y = mx + by = mx + b

m = —54

m = —-11 ( 4, 1 )

y = mx + by = mx + b

one solution no solution infinite solutions

ANY 2 lines that cross (intersect)

at one point.

ANY 2 lines that are parallel

(never intersect).

ANY 2 lines that are the exact

same line!

If one equation in a system was y = x + 3,

the “solution to a system” must be

a point on that line!

(must make the equation TRUE)

Complete the ordered pairs:

( 5, ___ )

( 2, ___ )

( 1, ___ )

( –3, ___ )

( 4, ___ )

( 3, ___ )

( 0, ___ )

( –5, ___ )

y = 5 + 3

8

5

4

0

7

6

3

–2

“is” is theEQUAL SIGN!

==

b + g = 29

10 less than meanssubtract 10.– 10

“twice the # of girls…

2g

Total of 29 students…Add boys & girls.

“The # of boys is…”

b = ( )

( 2g – 10 ) + g = 293g – 10 = 29

+ 10 + 103g = 39g = 13

13 girls

Use the 1st equation:

b = 2g – 10 b = 2(13) – 10 26 – 10

b = 1616 boys

( )

–2 ( 7 – 2y ) + 3y = 14 Dist. Prop.

– 14 + 4y + 3y = 14C.L.T.

– 14 + 7y = 14+ 14 + 14

7y = 28y = 4

Use the 2nd equation:

x = 7 – 2y

x = 7 – 2(4)

7 – 8

x = – 1

( , )–1 4

Since one equation has a variable by itself… SUBSTITUTION.Since one equation has a variable by itself… SUBSTITUTION.

( ) (( ) (– 1)– 1)

3x + 8y = 14 –3x + 4y = – 2

12y = 12y = 1

Use either equation:

3x – 4y = 23x – 4(1) = 2

3x – 4 = 2 + 4 + 4

3x = 6 x = 2

( , )2 1Both standard form… use elimination!Both standard form… use elimination!

19 people…add adults and students

a + s = 19

“5 hours” is EXTRA INFO!

adults cost $9 9a

students cost $4

4s everyone cost $111

+ = 111(( )) (-4)

– 4a – 4s = – 76 9a + 4s = 111

5a = 35a = 7

7 adults

The 1st equation looks easier:

a + s = 197 + s = 19–7 – 7

s = 12

12 students

Both standard form… Both standard form… use elimination!use elimination!

3/2 (-6) – 9 = – 18

3/2 (-3) – 9 = – 13.5

3/2 (0) – 9 = – 93/2 (3) – 9 = – 4.53/2 (6) – 9 = 0

– 4/3 (-6) + 8 =16

– 4/3 (-3) + 8 =12

– 4/3 (0) + 8 =8

– 4/3 (3) + 8 =4

– 4/3 (6) + 8 =0

Which ordered pair is the SAME in both tables?

( 6 , 0)

( 6 , 0 )

( )( )

4x – ( 2x – 5 ) = 7 Dist. Property

4x – 2x + 5 = 7C.L.T.

2x + 5 = 7 – 5 – 5 2x = 2

x = 1

Use the 1st equation:y = 2x – 5

y = 2(1) – 5 2 – 5

y = – 3

( , )1 –3Since one equation has a variable by itself… SUBSTITUTION.Since one equation has a variable by itself… SUBSTITUTION.

– 6x = – 54

x = 9 Use either equation:

– 2x + 8y = – 26

– 2(9) + 8y = – 26

– 18 + 8y = – 26

+ 18 + 18

8y = – 8

y = – 1

( , )9 – 1Both standard form… use elimination!Both standard form… use elimination!

( )( )

1 + x = 2x + 6 – 2x – 2x 1 – x = 6 – 1 – 1 – x = 5

x = – 5

Choose either equation:y = 1 + x

y = 1 + (–5)

y = – 4

( , )– 5 – 4

– 4

Since one equation has a variable by itself… SUBSTITUTION.Since one equation has a variable by itself… SUBSTITUTION.

add nickels & dimes n + d

103 coins

= 103nickels are

worth 0.05 ea.

0.05n dimes are worth 0.10 ea.

0.10d

All the coins are worth $8.00

+ = 8.00

The problem says to write the system…

NOT SOLVE IT!

Let c be packs of cards…and let t be tattoos.

Jose 4c + 3t Jose spent $11.45= 11.45

L.C. 1c + 4t L.C. spent $9.85= 9.85(( )) (– 4)

4c + 3t = 11.45– 4c – 16t = –39.40

– 13t = –27.95 t = 2.15$2.15 per tattoo

Use one of the equations:

c + 4t = 9.85c + 4(2.15) = 9.85c + 8.60 = 9.85

– 8.60 – 8.60 c = 1.25

$1.25 per pack of cards

Both standard form… Both standard form… use elimination!use elimination!

(( )) (–2)

2a + 2b = 16–2a – 2b = 16

0 = 32True? NO!

No Solution

No SolutionNo Solution

Both standard form… use elimination!Both standard form… use elimination!

How many less?(subtract)30 – 10

20

Animals total?(add)

30 + 10

40

How many times?(divide)30 ÷ 10

3

( , )4 3

Failure to prepare means you must be prepared to fail.

STUDY!STUDY!