Step 1) Solve the first equation for #x#:
#x + 3y - color(red)(3y) = 27 - color(red)(3y)#
#x + 0 = 27 - 3y#
#x = 27 - 3y#
Step 2) Substitute #(27 - 3y)# for #x# in the second equation and solve for #y#:
#13x - 6y = 36# becomes:
#13(27 - 3y) - 6y = 36#
#(13 * 27) - (13 * 3y) - 6y = 36#
#351 - 39y - 6y = 36#
#351 + (-39 - 6)y = 36#
#351 + (-45)y = 36#
#351 - 45y = 36#
#-color(red)(351) + 351 - 45y = -color(red)(351) + 36#
#0 - 45y = -315#
#-45y = -315#
#(-45y)/color(red)(-45) = -315/color(red)(-45)#
#(color(red)(cancel(color(black)(-45)))y)/cancel(color(red)(-45)) = 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 = 27 - 3y# becomes:
#x = 27 - (3 * 7)#
#x = 27 - 21#
#x = 6#
The solution is: #x = 6# and #y = 7#
