# How do you solve x+y= -3 and x+y=3?

Aug 23, 2015

$\left\{\begin{matrix}x = \emptyset \\ y = \emptyset\end{matrix}\right.$

#### Explanation:

Your system of equations will have no solution.

Notice that you have $x + y$ on the left side of both equations, but that the right side is different. The first equation has

$x + y = - 3$

and the second equation has

$x + y = 3$

If you try to replace $x + y$ from the first equation into the second, you will get

$3 \ne - 3$

An alternative approach is to notice that you're dealing with the equations of two lines. When you're solving a system of equations, you're essentially looking for the point in which those lines intersect.

In your case, these lines will never intersect because they are parralel lines.

graph{(y+x-3)(y+x+3)=0 [-10, 10, -5, 5]}