# How do you solve the system x + y = 4 and –x + y = 2 by graphing?

Mar 26, 2018

$\left(1 , 3\right)$
(Graph in explanation)

#### Explanation:

First, we need to set the equation so that $y$ is by itself.

For the first equation $x + y = 4$, we can subtract $x$ from both sides and get $y = 4 - x$.

For the second equation $- x + y = 2$, we can add $x$ on both sides of the equation and get $y = x + 2$.

Now we can graph this. We graph both equations on the same graph because to solve by graphing, we have to find the point(s) where the two graphs intersect:

The red line represents the equation $y = 4 - x$.
The blue line represents the equation $y = x + 2$.

As you can see, the equations intersect at the point $\left(1 , 3\right)$.

Therefore, the answer is $\left(1 , 3\right)$.

Hope this helps!