3x+ 2y = -6 ...........(1)

x + 3y = -2 ..............(2)

First we will solve algebraically.

Multiply (2) by -3 and add to (1).

==> 3x + 2y = -6

==> -3x -9y = 6

==> -7y = o ==> y= 0

==> 3x = -6 ==> x = -2

Then, the solution is the point (-2,0)

Now we will verify by graphing both lines.

3x+2y = -6 ( black line)

x+ 3y = -2 (red line)

You can see that both lines intersects at the point (-2, 0) which is the solution of the system.

3x+2y=-6, x+3y=-2

I'll start out with the second equation since it is easier for me that way:

x+3y=-2

subtract 3y from both sides:

x = -2 - 3y

now we know what x is (for now) plug it in as x into any of the problems above:

3(-2 - 3y) + 2y = -6

simplify:

-6 - 9y + 2y = -6

combine like terms:

-6 - 7y = -6

add 6 to both sides:

-7y = 0

divide

y = 0

plug in this result into any of the problems:

x+3(0) =-2

x = -2

( -2, 0)