How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent #2x + 2y = –6# and #3x – 2y = 11#?

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Answer 1 · 2017-09-04T16:38:40

See a solution process below:

Step 1) Solve the first equation for #x#:

#2x + 2y = -6#

#2x + 2y - color(red)(2y) = -6 - color(red)(2y)#

#2x + 0 = -6 - 2y#

#2x = -6 - 2y#

#(2x)/color(red)(2) = (-6 - 2y)/color(red)(2)#

#(color(red)(cancel(color(black)(2)))x)/cancel(color(red)(2)) = (-6)/color(red)(2) - (2y)/color(red)(2)#

#x = -3 - y#

Step 2) Substitute #(-3 - y)# for #x# in the second equation and solve for #y#:

#3x - 2y = 11# becomes:

#3(-3 - y) - 2y = 11#

#(3 xx -3) - (3 xx y) - 2y = 11#

#-9 - 3y - 2y = 11#

#-9 - 5y = 11#

#color(red)(9) - 9 - 5y = color(red)(9) + 11#

#0 - 5y = 20#

#-5y = 20#

#(-5y)/color(red)(-5) = 20/color(red)(-5)#

#(color(red)(cancel(color(black)(-5)))y)/cancel(color(red)(-5)) = -4#

#y = -4#

Step 3) Substitute #-4# for #y# in the solution to the first equation at the end of Step 1 and calculate #x#:

#x = -3 - y# becomes:

#x = -3 - (-4)#

#x = -3 + 4#

#x = 1#

The Solution Is: #x = 1# and #y = -4# or #(1, -4)#