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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