Question

What are x and y if `4x-4y=-16` and `x-2y=-12`?

Answer 1

`x = 4`, `y = 8`

Explanation:

There are many ways to solve a system of linear equations.
One of those goes like this:

Take the equation that looks easier to you and solve it for `x` or `y`, whichever is easier.
In this case, if I were you, I would definitely take `x - 2y = -12` and solve it for `x`:

`x - 2y = - 12`
`<=> x = 2y - 12`

Now, plug `2y - 12` for `x` in the other equation:

`4*(2y-12) - 4y = -16`

...simplify the left side:
`<=> 8y - 48 - 4y = -16`
`<=> 4y - 48 = -16`

... add `48` on both sides:
`<=> 4y = 48 - 16`
`<=> 4y = 32`

... divide by 4 on both sides:
`<=> y = 8`

Now that you have the solution for `y`, you just need to plug this value into one of the two equations (again, whichever is easier) and compute `x`:

`x - 2* 8 = - 12`
`<=> x = 16 - 12`
`<=> x = 4`