How do you solve the following system?: # -8x+3y=12 , 8x-9y= 12 #

1 Answer
Mar 14, 2018

Answer:

#x=-3, y=-4#

Explanation:

Given: #8x-9y=12#. Solve for x.
#8x-9y+9y=12+9y#
#8x=12+9y#
#(8x)/8=(12+9y)/8#

#x=(12+9y)/8#

Substitute this into the other equation:

#-8x+3y=12#

#-8((12+9y)/8)+3y=12#

#-1(12+9y)+3y=12#

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

#-12-6y=12#

#-12-6y+12=12+12#

#-6y=24#

#(-6y)/-6=24/-6#

#y=-4#

Substitute into original equation:

#8x-(9*-4)=12#

#8x+36=12#

#8x+36-36=12-36#

#8x =-24#

#(8x)/8=-24/8#

#x=-3#

To check, substitute both answers into both the formulas:

#-8*-3+3*-4=24-12=12# True

#8*-3-9*-4=-24+36=12# True