How do you solve the system of equations 8x+7y=-518x+7y=−51 and x-y=3x−y=3?

1 Answer
seph
Oct 31, 2016

x = -2x=−2
y = -5y=−5

Explanation:

Scale either equation (or both) such that the coefficient of one of the variables will have the same absolute value for both equations

[1] 8x + 7y = -51[1]8x+7y=−51
[2] x - y = 3[2]x−y=3

Multiply [2][2] by 77

[3] => 7(x - y = 3)[3]⇒7(x−y=3)

[3] => 7x - 7y = 21[3]⇒7x−7y=21

Note that the absolute value of yy's coefficient is 77 for both [1][1] and [3][3]. If we add [1][1] and [3][3], we have

[1] 8x +7y = -51[1]8x+7y=−51
[3] 7x - 7y = 21[3]7x−7y=21

[4] => 15x + 0y = -30[4]⇒15x+0y=−30

=> x = -2⇒x=−2

Now that we know the value of xx, use it in either [1][1], [2][2], or [3][3] to get yy. Let's use [2][2]

[2] x - y = 3[2]x−y=3
=> -2 - y = 3⇒−2−y=3
=> y = -5⇒y=−5

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