Step 1) Solve the first equation for x:
3x +3y = -9
(3x +3y)/color(red)(3) = -9/color(red)(3)
(3x)/color(red)(3) +(3y)/color(red)(3) = -3
x + y = -3
x + y - color(red)(y) = -3 - color(red)(y)
x + 0 = -3 - y
x = -3 - y
Step 2) Substitute (-3 - y) for x in the second equation and solve for y:
6x + 2y = 2 becomes:
6(-3 - y) + 2y = 2
(6 xx -3) - (6 xx y) + 2y = 2
-18 - 6y + 2y = 2
-18 + (-6 + 2)y = 2
-18 + (-4)y = 2
-18 - 4y = 2
-18 + color(red)(18) - 4y = 2 + color(red)(18)
0 - 4y = 20
-4y = 20
(-4y)/color(red)(-4) = 20/color(red)(-4)
(color(red)(cancel(color(black)(-4)))y)/cancel(color(red)(-4)) = -5
y = -5
Step 3) Substitute -5 for y in the solution to the first equation at the end of Step 1 and calculate x:
x = -3 - y becomes:
x = -3 - (-5)
x = -3 + 5
x = 2
The Solution Is:
x = 2 and y = -5
Or
(2, -5)