How do you solve 8x - 8y = 16 and 4x + 4y = -72 ?

1 Answer

Work with one equation to get a term in the other, then substitute in, to get the system x=-8, y=-10

Explanation:

We have a system of 2 equations:

8x-8y=16
4x+4y=-72

Since this is in the substitution method category, we'll use that method.

If we take the second equation and multiply both sides by 2, we can get the term 8x. We can take what 8x will equal and substitute it into the first equation:

(4x+4y)(2)=(-72)(2)

8x+8y=-144

8x=-144-8y

So let's now substitute. Starting with the first equation:

8x-8y=16

-144-8y-8y=16

-16y=160

y=-10

We can now solve for x. I'm going to do it with both equations so that we can make sure we didn't make a mistake (if we get 2 different answers in checking the 2 equations, we did!)

8x-8y=16

8x-8(-10)=16

8x+80=16

8x=-64

x=-8

and now the other one:

4x+4y=-72

4x+4(-10)=-72

4x-40=-72

4x=-32

x=-8

x=-8, y=-10