Question

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

Answer 1

`x = -2`
`y = -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`
`[2] x - y = 3`

Multiply `[2]` by `7`

`[3] => 7(x - y = 3)`

`[3] => 7x - 7y = 21`

Note that the absolute value of `y`'s coefficient is `7` for both `[1]` and `[3]`. If we add `[1]` and `[3]`, we have

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

`[4] => 15x + 0y = -30`

`=> x = -2`

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

`[2] x - y = 3`
`=> -2 - y = 3`
`=> y = -5`