Step 1) Solve the first equation for #x#:
#2x + 4y = -8#
#(2x + 4y)/color(red)(2) = -8/color(red)(2)#
#(2x)/color(red)(2) + (4y)/color(red)(2) = -4#
#x + 2y = -4#
#x + 2y - color(red)(2y) = -4 - color(red)(2y)#
#x + 0 = -4 - 2y#
#x = -4 - 2y#
Step 2) Substitute #(-4 - 2y)# for #x# in the second equation and solve for #y#:
#2x + 7y = -20# becomes:
#2(-4 - 2y) + 7y = -20#
#(2 xx -4) - (2 xx 2y) + 7y = -20#
#-8 - 4y + 7y = -20#
#-8 + (-4 + 7)y = -20#
#-8 + 3y = -20#
#-8 + color(red)(8) + 3y = -20 + color(red)(8)#
#0 + 3y = -12#
#3y = -12#
#(3y)/color(red)(3) = -12/color(red)(3)#
#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 = -4 - 2y# becomes:
#x = -4 - (2 xx -4)#
#x = -4 - (-8)#
#x = -4 + 8#
#x = 4#
The Solution Is:
#x= 4# and #y = -4#
Or
#(4, -4)#