Step 1) Solve the second equation for #x#:
#-3x - 6y = -24#
#-3x - 6y + color(red)(6y) = -24 + color(red)(6y)#
#-3x - 0 = -24 + 6y#
#-3x = -24 + 6y#
#(-3x)/color(red)(-3) = (-24 + 6y)/color(red)(-3)#
#(color(red)(cancel(color(black)(-3)))x)/cancel(color(red)(-3)) = (-24)/color(red)(-3) + (6y)/color(red)(-3)#
#x = 8 - 2y#
Step 2) Substitute #8 - 2y# for #x# in the first equation and solve for #y#:
#2x + 3y = 21# becomes:
#2(8 - 2y) + 3y = 21#
#(2 xx 8) - (2 xx 2y) + 3y = 21#
#16 - 4y + 3y = 21#
#16 + (-4 + 3)y = 21#
#16 - y = 21#
#16 - y - color(red)(16) = 21 - color(red)(16)#
#16 - color(red)(16) - y = 5#
#0 - y = 5#
#-y = 5#
#-1 xx -y = -1 xx 5#
#y = -5#
Step 3) Substitute #-5# for #y# in the solution to the second equation at the end of Step 1 and calculate #x#:
#x = 8 - 2y# becomes:
#x = 8 - (2 xx -5)#
#x = 8 - (-10)#
#x = 8 + 10#
#x = 18#
The solution is: #x = 18# and #y = -5# or #(18, -5)#
