How do you solve #2x+3y=21# and #-3x-6y=-24#?

1 Answer
Feb 26, 2017

Answer:

See the entire solution process below:

Explanation:

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)#