Question

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

Answer 1

↓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}