Step 1) Solve the first equation for #x#:
#x + y = 10#
#x + y - color(red)(y) = 10 - color(red)(y)#
#x + 0 = 10 - y#
#x = 10 - y#
Step 2) Substitute #10 - y# for #x# in the second equation and solve for #y#:
#5x - y = 8# becomes:
#5(10 - y) - y = 8#
#(5 xx 10) - (5 xx y) - y = 8#
#50 - 5y - y = 8#
#50 - 6y = 8#
#-color(red)(50) + 50 - 6y = -color(red)(50) + 8#
#0 - 6y = -42#
#-6y = -42#
#(-6y)/color(red)(-6) = -42/color(red)(-6)#
#(color(red)(cancel(color(black)(-6)))y)/cancel(color(red)(-6)) = 7#
#y = 7#
Step 3) Substitute #-7# for #y# in the solution to the first equation at the end of Step 1 and calculate #x#:
#x = 10 - y# becomes:
#x = 10 - 7#
#x = 10 - 7#
#x = 3#
The solution is: #x = 3# and #y = 7# or #(3, 7)#
