Step 1) Solve the first equation for #x#:
#5x - 5y = 10#
#5x - 5y + color(red)(5y) = 10 + color(red)(5y)#
#5x - 0 = 10 + 5y#
#5x = 10 + 5y#
#(5x)/color(red)(5) = (10 + 5y)/color(red)(5)#
#(color(red)(cancel(color(black)(5)))x)/cancel(color(red)(5)) = 10/color(red)(5) + (5y)/color(red)(5)#
#x = 2 + y#
Step 2) Substitute #2 + y# for #x# in the second equation and solve for #y#:
#-4x - 14y = 28# becomes:
#-4(2 + y) - 14y = 28#
#-8 - 4y - 14y = 28#
#color(red)(8) - 8 - (4 + 14)y = color(red)(8) + 28#
#0 - 18y= 36#
#-18y = 36#
#(-18y)/color(red)(-18) = 36/color(red)(-18)#
#(color(red)(cancel(color(black)(-18)))y)/cancel(color(red)(-18)) = -2#
#y = -2#
Step 3) Substitute #-2# for #y# in the solution to the first equation at the end of Step 1 and calculate #x#:
#x = 2 + y# becomes:
#x = 2 + (-2)#
#x = 0#
The solution is: #x = 0# and #y = -2#
