Step 1) Solve the second equation for #x#:
#x - 2y = 13#
#x - 2y + color(red)(2y) = 13 + color(red)(2y)#
#x - 0 = 13 + 2y#
#x = 13 + 2y#
Step 2) Substitute #(13 + 2y)# for #x# in the first equation and solve for #y#:
#3x + 2y = -5# becomes:
#3(13 + 2y) + 2y = -5#
#(3 * 13) + (3 * 2y) + 2y = -5#
#39 + 6y + 2y = -5#
#39 + (6 + 2)y = -5#
#39 + 8y = -5#
#39 - color(red)(39) + 8y = -5 - color(red)(39)#
#0 + 8y = -44#
#8y = -44#
#(8y)/color(red)(8) = -44/color(red)(8)#
#(color(red)(cancel(color(black)(8)))y)/cancel(color(red)(8)) = -(4 xx 11)/color(red)(4 xx 2)#
#y = -11/2#
Step 3) Substitute #-11/2# for #y# in the solution to the second equation at the end of Step 1 and calculate #x#:
#x = 13 + 2y# becomes:
#x = 13 + (2 xx -11/2)#
#x = 13 + (-11)#
#x = 2#
The Solution Is:
#x = 2# and #y = -11/2#
Or
#(2, -11/2)#
