Step 1) Solve the second equation for #x#:
#2x - 2y = -4#
#2x - 2y + color(red)(2y) = -4 + color(red)(2y)#
#2x - 0 = -4 + 2y#
#2x = -4 + 2y#
#(2x)/color(red)(2) = (-4 + 2y)/color(red)(2)#
#(color(red)(cancel(color(black)(2)))x)/cancel(color(red)(2)) = -4/color(red)(2) + (2y)/color(red)(2)#
#x = -2 + y#
Step 2) Substitute #(-2 + y)# in the first equation for #x# and solve for #y#:
#4x - 6y = -8# becomes:
#4(-2 + y) - 6y = -8#
#(4 xx -2) + (4 xx y) - 6y = -8#
#-8 + 4y - 6y = -8#
#-8 + (4 - 6)y = -8#
#-8 + (-2)y = -8#
#-8 - 2y = -8#
#color(red)(8) - 8 - 2y = color(red)(8) - 8#
#-2y = 0#
#(-2y)/color(red)(-2) = 0/color(red)(-2)#
#(color(red)(cancel(color(black)(-2)))y)/cancel(color(red)(-2)) = 0#
#y = 0#
Step 3) Substitute #0# for #y# in the solution to the second equation at the end of Step 1 and calculate #x#:
#x = -2 + y# becomes:
#x = -2 + 0#
#x = -2#
The Solution Is: #x = -2# and #y = 0# or #(-2, 0)#