Question

50 POINTS!!!

Solve by the linear combination method.

2x + 8y = –2
5x + 6y = 9




(3, –1)


(–2, 2)


(–2, 7)


(–1, 3)

Answer 1

To find the y:
2x + 8y = –2
5x + 6y = 9

(2x + 8y = –2) -5
(5x + 6y = 9) 2
-10x - 40y = 10
10x + 12y = 18
-28y = 28
y = -1
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To find the x:
5x + 6y = 9

5x + 6(-1) = 9
5x - 6 = 9
5x = 15
x = 3
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Check:
2x + 8y = –2
2(3) + 8(-1) = -2
6 - 8 = -2
-2 = -2
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Solution: (3,-1)

Answer 2

2x + 8y = –2 --------- (1)
5x + 6y = 9 --------- (2)

(1) x 5 : 10x + 40y = -10 ----------- (1a)
(2) x 2 : 10x + 12y = 18 ----------- (2a)

(1a) - (2a) : 28y = -28
y = -1

Substitute y = -1 into (1)
2x + 8(-1) = –2
2x - 8 = -2
2x = 6
x = 3

Answer : (3, -1) (Answer A)