How do you solve the system of equations #-4x - 12y = - 16# and #- 3x + 3y = 12#?

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Answer 1 · 2016-11-18T12:58:22

#y = 2# and #x = -2#

Step 1) Solve the first equation for #x# while keeping the equation balanced:

#-4x - 12y + 12y = -16 + 12y#

#-4x = -16 + 12y#

#(-4x)/-4 = (-16 + 12y)/-4#

#x = (-16)/-4 + (12y)/-4#

#x = 4 - 3y#

Step 2) Substitute #4 - 3y# for #x# in the second equation and solve for #x# while keeping the equation balanced:

#-3(4 - 3y) + 3y = 12#

#-12 + 9y + 3y = 12#

#-12 + 12y = 12#

#-12 + 12y + 12 = 12 + 12#

#12y = 24#

#(12y)/12 = 24/12#

#y = 2#

Step 3) Substitute #2# for #y# in the solution for the first equation and calculate #x#:

#x = 4 - (3*2)#

#x = 4 - 6#

#x = -2#