Step 1) Solve the first equation for #x#:
#x + 4y = 5#
#x + 4y - color(red)(4y) = 5 - color(red)(4y)#
#x + 0 = 5 - 4y#
#x = 5 - 4y#
Step 2) Substitute #(5 - 4y)# for #x# in the second equation and solve for #y#:
#3x - 2y = -13# becomes:
#3(5 - 4y) - 2y = -13#
#(3 * 5) - (3 * 4y) - 2y = -13#
#15 - 12y - 2y = -13#
#15 + (-12 - 2)y = -13#
#15 + (-14)y = -13#
#15 - 14y = -13#
#-color(red)(15) + 15 - 14y = -color(red)(15) - 13#
#0 - 14y = -28#
#-14y = -28#
#(-14y)/color(red)(-14) = (-28)/color(red)(-14)#
#(color(red)(cancel(color(black)(-14)))y)/cancel(color(red)(-14)) = 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 = 5 - 4y# becomes:
#x = 5 - (4 * 2)#
#x = 5 - 8#
#x = -3#
The Solution Is: #x = -3# and #y = 2# or #(-3, 2)#
