Question

How do you solve the following system: `-x+6y=12, x-4y=2`?

Answer 1

`color(white)(xx)x=30`, `y=7`

Explanation:

`color(white)(xx)-x+6y=12, x-4y=2`

`color(white)(xx)-x+6y=12<=>y=(x+12)/6`
`color(white)(xx)x-4y=2<=>y=(x-2)/4`

`color(white)(xx)y=(x+12)/6`
`=>color(blue)((x-2)/4)=(x+12)/6`

Multiply both side by `color(red)12`:
`color(white)(xx)color(red)(12xx)(x-2)/4=color(red)(12xx)(x+12)/6`
`=>3x-6=2x+24`

Add `color(red)(-2x+6)` to both side:
`color(white)(xx)3x-6color(red)(-2x+6)=2x+24color(red)(-2x+6)`

`color(white)(xx)x=30`

`color(white)(xx)y=(x-2)/4`

`color(white)(xxx)=(color(red)30-2)/4`
`color(white)(xxx)=(color(red)28)/4`
`color(white)(xxx)=7`