Question

How do you solve `x + y = -7` and `3x + y = -9`?

Answer 1

`x = -1`; `y = -6`

Explanation:

You could solve this system of equations by using the multiplication method.

To do that, start by multiplying both sides of the first equation by `-3`.

`-3 * (x+y) = -3 * (-7)`

`-3x - 3y = 21`

The system of equations will now be

`{(-3x -3y = 21), (3x + y = -9) :}`

Next, add left sides and the right sides of the two equations separately to eliminate the terms that contain `x`

`-color(red)(cancel(color(black)(3x))) - 3y + color(red)(cancel(color(black)(3x))) + y = 21 - 9`

`-2y = 12`

Divide both sides of the equation by `-2` to get the value of `y`

`(-color(red)(cancel(color(black)(2)))y)/(-color(red)(cancel(color(black)(2)))) = 12/(-2) => y = color(green)(-6)`

Now that you know the value of `y`, use it in one of the two equations to determine the value of `x`

`3x + y = -9`

`3x + (-6) = -9`

This is equivalent to

`3x = -9 + 6 = -3`

Now divide both sides of this equation by `3` to get the value of `x`

`(color(red)(cancel(color(black)(3)))x)/color(red)(cancel(color(black)(3))) = (-3)/3 => x = color(green)(-1)`

The two solutions are

`{(x=-1), (y=-6) :}`