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Key answers
A. SOLVING LINEAR EQUATIONS BY SUBSTITUTION & ELIMINATION
METHOD8. In the system of this type, multiply so that
the numerators are equal and the variable with equal numerators can be eliminated.
SOLUTION:Multiply the 1st equation by 4. Then add the
result to the 2nd equation.
202012
553
4553
yxyxyx
A. SOLVING LINEAR EQUATIONS BY SUBSTITUTION & ELIMINATION
METHODSOLUTION:Multiply the 1st equation by 4. Then add the
result to the 2nd equation.
3
521
35
2135
y
y
y
+
3
521
35
2135
y
y
y
A. SOLVING LINEAR EQUATIONS BY SUBSTITUTION & ELIMINATION
METHODSOLUTION:To find x, substitute the value of y in any
equation.
2
3
23
533
55
35
3
x
x
xx
The solution is (3/2, 5/3)
B. CONSSITENT,INCONSISTENT, DEPENDENT1. 7: 14 = (-2) : (-4) ≠ 7:6 (inconsistent)
6. 2:6 = 1:3 = 5:15 (dependent)
The rest are consistent
C. CONSSITENT,INCONSISTENT, DEPENDENT1. Any value of y will make the system consistent as 1: 3 ≠ (-2) : 1
2. 2:4 = (-1):(-2) =7:kIf k =14, the system will be dependent; if k ≠ 14, the system is inconsistent.
C. CONSSITENT,INCONSISTENT, DEPENDENT
3. 3:1 = 9:3 =6:kIf k =2, the system will be dependent; if k ≠ 2, the system is inconsistent.
D. PROBLEM SOLVING1. X = 30, the smaller numberX + 15 = 45, the bigger number
2. let x be the smaller number 900-x, the larger 0.04(900-x) + 0.07x = 48 x = 400 (smaller number) & 900-x = 500, (bigger number)
D. PROBLEM SOLVING3. X = P60, the cost of the belts
y= P130, the cost of the hats
4. let x be the tens digit 11-x, the ones digit x = 3 11- x = 8 , therefore the number is 38.
D. PROBLEM SOLVING5. X = age of the son 4x= age of Mr. CarlosSo, x = 10 years, 4x = 40 years
6. let x be the money of A y pesos, the money of B x = 10 & y = 30
Challenge 1. let x meter (m) be the width of the pool The length be 1.5 x. The outer width is (x + 2)m The outer length is (1.5x + 2)m
The area of a path = (1.5x + 2)(x+2)- x(1.5 x) = 44
5x + 4 = 44
5x = 40 x = 8 m, the width of the
pool 1.5 x = 12 m, the length of
the pool
Challenge 2. let x be the number of the guest
½ x ,the number of bowls of rice
1/3 x ,the number of bowls of broth ¼ x ,the number of bowls of meat
6x + 4x + 3x = 12(65) 13x = 12 (65)
x = 60, the number of guest
65432
xxx
Challenge 3. let x be pesos the cost of bracelet
y, the cost of watchband
z ,the cost of a locket x + y = 500 (eq. 1) y + z = 600 (eq. 2) z + x = 700 (eq. 3)2x +2y +2z = 1800 x +y +z = 900 rewrite eq. 1, y = 500 - x
x +y +z = 900
x + 500-x +z =900
z= 900-500z = P400 y = P200 x = P300