Step 1) Solve the first equation for #x#:
#5x + 5y = -10#
#(5x + 5y)/color(red)(5) = -10/color(red)(5)#
#(5x)/color(red)(5) + (5y)/color(red)(5) = -2#
#x + y = -2#
#x + y - color(red)(y) = -2 - color(red)(y)#
#x + 0 = -2 - y#
#x = -2 - y#
Step 2) Substitute #(-2 - y)# for #x# in the second equation and solve for #y#:
#-4x + 2y = -10# becomes:
#-4(-2 - y) + 2y = -10#
#(-4 xx -2) + (-4 xx -y) + 2y = -10#
#8 + 4y + 2y = -10#
#8 + (4 + 2)y = -10#
#8 + 6y = -10#
#8 - color(red)(8) + 6y = -10 - color(red)(8)#
#0 + 6y = -18#
#6y = -18#
#(6y)/color(red)(6) = -18/color(red)(6)#
#(color(red)(cancel(color(black)(6)))y)/cancel(color(red)(6)) = -3#
#y = -3#
Step 3) Substitute #-3# for #y# in the solution to the first equation at the end of Step 1 and calculate #x#:
#x = -2 - y# becomes:
#x = -2 - (-3)#
#x = -2 + 3#
#x = 1#
The Solution Is:
#x = 1# and #y = -3#
Or
#(1, -3)#
