Step 1) Solve the first equation for #y#:
#4x - y = -24#
#4x - y + color(blue)(y) + color(red)(24) = -24 + color(red)(24) + color(blue)(y)#
#4x - 0 + 24 = 0 + y#
#4x + 24 = y#
#y = 4x + 24#
Step 2) Substitute #(4x + 24)# for #y# in the second equation and solve for #x#:
#6x + 3y = -9# becomes:
#6x + 3(4x + 24) = -9#
#6x + (3 xx 4x) + (3 xx 24) = -9#
#6x + 12x + 72 = -9#
#(6 + 12)x + 72 = -9#
#18x + 72 = -9#
#18x + 72 - color(red)(72) = -9 - color(red)(72)#
#18x + 0 = -81#
#18x = -81#
#(18x)/color(red)(18) = -81/color(red)(18)#
#(color(red)(cancel(color(black)(18)))x)/cancel(color(red)(18)) = -(9 xx 9)/color(red)(9 xx 2)#
#x = -9/2#
Step 3) Substitute #-9/2# for #x# in the solution to the first equation at the end of Step 1 and calculate #y#:
#y = 4x + 24# becomes:
#y = (4 xx -9/2) + 24#
#y = -36/2 + 24#
#y = -18 + 24#
#y = 6#
The Solution Is: #x = -9/2# and #y = 6# or #(-9/2, 6)#
