Question

How do you solve `2x-y=-1` and `x+y=-5`?

Answer 1

`(x,y) = (-2,-3)`

Explanation:

There are several ways to solve a system, so it's always best to choose the simplest method to avoid what we call "nuking mosquitos", i.e. using a complex solution for a simple problem

In this case, I think the easiest way is to sum the two equations: adding the left and right sides, we have

`2x-y+x+y = -1-5`

and thus

`3x=-6`

This should make clear why I chose to sum the two equations: we cancel `y` out, and can easily solve for `x`:

`3x=-6 \implies x = -2`

Once we know the value of `x`, we can obtain `y` by substitution:

`x+y=-2 \implies -2+y=-5 \implies y=-3`