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)#
