Question

How do solve the following linear system?: `-6x+6y=6 , x+2y=5`?

Answer 1

`x=1 and y=2`

Explanation:

`color(white)(xxxxx)-6x+6y =6" "....A`
`color(white)(xxxxxxxx)color(blue)(x)+2y=5" "....B`
`Adiv 6 rarr color(blue)(-x)+y =1" "....C`

we now have a perfect scenario where `color(blue)(x) and color(blue)(-x)` are additive inverses. Their sum is `0`
Add the equations `A and C` together.

`A+C rarr color(white)(xxxx)3y=6`
`color(white)(xxxxxxxxxxxx)y=2`

Substitute into `B:" "x+2(2)=5`
`color(white)(xxxxxxxxxxxxxxxxxx)x=1`

Check in `C`

`(-1)+(2) =1" "....C`