Step 1) Solve the first equation for #x#:
#8x - 8y = -16#
#(8x - 8y)/color(red)(8) = -16/color(red)(8)#
#(8x)/color(red)(8) - (8y)/color(red)(8) = -2#
#x - y = -2#
#x - y + color(red)(y) = color(red)(y) - 2#
#x - 0 = y - 2#
#x = y - 2#
Step 2) Substitute #y - 2# for #x# in the second equation and solve for #y#:
#-2x + 4y = 14# becomes:
#-2(y - 2) + 4y = 14#
#(-2 * y) - (-2 * 2) + 4y = 14#
#-2y + 4 + 4y = 14#
#4y - 2y + 4 = 14#
#(4 - 2)y + 4 = 14#
#2y + 4 = 14#
#2y + 4 - color(red)(4) = 14 - color(red)(4)#
#2y + 0 = 10#
#2y = 10#
#(2y)/color(red)(2) = 10/color(red)(2)#
#(color(red)(cancel(color(black)(2)))y)/cancel(color(red)(2)) = 5#
#y = 5#
Step 3) Substitute #5# for #y# in the solution to the first equation at the end of Step 1 and calculate #x#:
#x = y - 2# becomes:
#x = 5 - 2#
#x = 3#
The solution is: #x = 3# and #y = 5# or #(3, 5)#