Question

How do you solve the system `x - 3y = -3`, `x + 3y = 9`?

Answer 1

`(3,2)`

Explanation:

We can use linear combination.

Add the two equations together (notice that the `y` terms will cancel out):

`x-3y=-3`
`x+3y=9`
`2x=6`

Therefore, if we divide both sides by `2`, we see that `x=3`. We can then plug `3` back into either equation for `x` in order to solve for `y`.

(Plugging into the first equation:)
`3-3y=-3`
`-3y=-6`
`y=2`

Since `x=3` and `y=2`, we can write our answers in an ordered pair: `(3,2)`.