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

Oct 2, 2016

$\left(x , y\right) = \left(- 2 , - 3\right)$

#### 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

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

and thus

$3 x = - 6$

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

$3 x = - 6 \setminus \implies x = - 2$

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

$x + y = - 2 \setminus \implies - 2 + y = - 5 \setminus \implies y = - 3$