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Rearrange the first equation until you have y written as some function of x, then plug the answer you have for y into the second equation. Now you can solve that equation for x. Then take your new value for x and sub it into either equation. You will get your value of y.

Here are the steps:

-6x + y= -12 (1)

7x+8y=14 (2)

Rearrange (1):

y = -6 (2+x)

Plug into (2)

7x+8(-6(2+x))=14 -> 7x-48(2+x) = 14 -> 7x-96+48x=14 -> 55x = 110

Thus, x = 2.

Take this value of x and plug it into either equation. It will generate a value for y.

Plug x = 2 into (1):

-6(2)+y=-12

Therefore, y = 0.

Done.

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Q: How do you find the solution of this system of equation -6x plus y equals -12 7x plus 8y equals 14?
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