# How do you solve the system 2x + 3y = -6  and x - 3y = 6 by graphing?

May 20, 2017

↓See below↓

#### Explanation:

A linear graph needs to have the $y$ term on its own. To do that, for the first equation, let us subtract $2 x$ from both sides.
$3 y = - 2 x - 6$
To isolate $y$, let's divide both sides of the equation by 3.
$y = - \frac{2}{3} x - 2$
We have our first graph ↓
graph{y=-2/3x-2 [-10, 10, -5, 5]}

To graph our second equation, let's subtract $x$ from both sides.

$- 3 y = - x - 6$
Then, divide by $- 3$ to isolate $y$
$y = \frac{x}{3} + 2$

We have our second graph ↓
graph{y=x/3+2 [-10, 10, -5, 5]}

Combine the two graphs.

The point where the 2 graphs intersect is the solution to this system of equations.

graph{(y-x/3-2)(y+2/3x+2)=0}