Step 1) Solve the second equation for y:
3x + y = -20
3x - color(red)(3x) + y = -color(red)(3x) - 20
0 + y = -3x - 20
y = -3x - 20
Step 2) Substitute (-3x - 20) for y in the first equation and solve for x:
9x - 6y = 3 becomes:
9x - 6(-3x - 20) = 3
9x - (6 xx -3x) - (6 xx -20) = 3
9x - (-18x) - (-120) = 3
9x + 18x + 120 = 3
(9 + 18)x + 120 = 3
27x + 120 = 3
27x + 120 - color(red)(120) = 3 - color(red)(120)
27x + 0 = -117
27x = -117
(27x)/color(red)(27) = -117/color(red)(27)
(color(red)(cancel(color(black)(27)))x)/cancel(color(red)(27)) = -(9 xx 13)/color(red)(9 xx 3)
x = -(color(red)(cancel(color(black)(9))) xx 13)/color(red)(color(black)(cancel(color(red)(9))) xx 3)
x = -13/3
Step 3) Substitute -13/3 for x in the solution to the second equation at the end of Step 1 and calculate y:
y = -3x - 20 becomes:
y = -(3 xx -13/3) - 20
y = -(-13) - 20
y = 13 - 20
y = -7
The Solution Is:
x = -13/3 and y = -7
Or
(-13/3, -7)
