Step 1) Solve the first equation for #x#:
#x - 2y = 8#
#x - 2y + color(red)(2y) = 8 + color(red)(2y)#
#x - 0 = 8 + 2y#
#x = 8 + 2y#
Step 2) Substitute #(8 + 2y)# for #x# in the second equation and solve for #y#:
#x + y = -1# becomes:
#(8 + 2y) + y = -1#
#8 + 2y + 1y = -1#
#8 + (2 + 1)y = -1#
#8 + 3y = -1#
#-color(red)(8) + 8 + 3y = -color(red)(8) - 1#
#0 + 3y = -9#
#3y = -9#
#(3y)/color(red)(3) = -9/color(red)(3)#
#(color(red)(cancel(color(black)(3)))y)/cancel(color(red)(3)) = -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 = 8 + 2y# becomes:
#x = 8 + (2 * -3)#
#x = 8 + (-6)#
#x = 2#
The solution is: #x = 2# and #y = -3# or #(2, -3)#
Because there is at least one point in common these equations are consistent.