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

1 Answer
May 20, 2017

Answer:

↓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 #2x# from both sides.
#3y=-2x-6#
To isolate #y#, let's divide both sides of the equation by 3.
#y=-2/3x-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.

#-3y=-x-6#
Then, divide by #-3# to isolate #y#
#y=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}