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