Question

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

Answer 1

`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`