Step 1) Solve the first equation for #x#:
#2x + 2y = -6#
#2x + 2y - color(red)(2y) = -6 - color(red)(2y)#
#2x + 0 = -6 - 2y#
#2x = -6 - 2y#
#(2x)/color(red)(2) = (-6 - 2y)/color(red)(2)#
#(color(red)(cancel(color(black)(2)))x)/cancel(color(red)(2)) = (-6)/color(red)(2) - (2y)/color(red)(2)#
#x = -3 - y#
Step 2) Substitute #(-3 - y)# for #x# in the second equation and solve for #y#:
#3x - 2y = 11# becomes:
#3(-3 - y) - 2y = 11#
#(3 xx -3) - (3 xx y) - 2y = 11#
#-9 - 3y - 2y = 11#
#-9 - 5y = 11#
#color(red)(9) - 9 - 5y = color(red)(9) + 11#
#0 - 5y = 20#
#-5y = 20#
#(-5y)/color(red)(-5) = 20/color(red)(-5)#
#(color(red)(cancel(color(black)(-5)))y)/cancel(color(red)(-5)) = -4#
#y = -4#
Step 3) Substitute #-4# for #y# in the solution to the first equation at the end of Step 1 and calculate #x#:
#x = -3 - y# becomes:
#x = -3 - (-4)#
#x = -3 + 4#
#x = 1#
The Solution Is: #x = 1# and #y = -4# or #(1, -4)#