Question

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

Answer 1

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`