How do you solve the following system: #2x-6y=-12 , 3x -2y=24 #?

1 Answer
Özgür Özer
Dec 15, 2015

#color(white)(xx)x=12# and #y=6#

Explanation:

#color(white)(xx)2x-6y=-12#, #3x-2y=24#

#{(2x-6y=-12<=>y=(x+6)/3),(3x-2y=24<=>y=(3x-24)/2):}#

#color(white)(xx)y=(x+6)/3#
#=>color(red)((3x-24)/2)=(x+6)/3#

Multiply both sides by #color(red)6#:
#color(white)(xx)color(red)(6xx)(3x-24)/2=color(red)(6xx)(x+6)/3#
#=>9x-72=2x+12#

Add #color(red)(-2x+72)# to both sides:
#color(white)(xx)9x-72color(red)(-2x+72)=2x+12color(red)(-2x+72)#
#=>7x=84#

Multiply both sides by #color(red)(1/7)#:
#color(white)(xx)color(red)(1/7xx)7x=color(red)(1/7xx)84#
#=>x=12#

#color(white)(xx)y=(x+6)/3#
#color(white)(xxx)=(color(red)12+6)/3#
#color(white)(xxx)=6#

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