Question

How do you solve the system of equations `-x-2y=9` and `3x+2y=-3` by adding or subtracting?

Answer 1

See the steps below

Explanation:

The first thing you want to do is multiply one equation through by a constant value that will cause one of the variables to have the same coefficient (the value to the left of the variable), but with opposite sign. I will use the `x`-variable:

Multiply the first equation by 3 (every term)

`(3)(-x-2y=9)` becomes `-3x-6y=27`

Next, add the two equations, which means add like terms

`-3x-6y=27`
+`3x+2y=-3`

Gives us `-4y=24` meaning `y=-6`

Notice how the `x` term did not appear in this result. This is what makes it possible to solve the equation - there i only one variable in it.

Now, pick either of the original equations and substitute in `y=-6`

You will find that `x=3`