# How do you solve the following linear system -x + y = 2 , x + 3y =2 ?

Mar 17, 2018

$\left(- 1 , 1\right)$

#### Explanation:

We have:

$\left(\begin{matrix}- x + y = 2 \\ x + 3 y = 2\end{matrix}\right)$

We can add the two equations. See how the $x$ variable cancels out, as $- x + x = 0$.

$4 y = 4$

$y = 1$

We can input this into the first equation:

$- x + 1 = 2$

$- x = 1$

$x = - 1$

So the solution is $\left(- 1 , 1\right)$.

Another cool way to solve these is to graph them. Their point of intersection is the solution to this system: