Question

How do you solve `-2x + y = 1` and `-4x + y = -1` using substitution?

Answer 1

`(x,y)=(color(cyan)(1,3))`

Explanation:

If
`color(white)("XXX")-2x+y=1`
then
`color(white)("XXX")color(red)(y)=color(blue)(1+2x)`

Since we are also told that
[3]`color(white)("XXX")-4x+color(red)(y)=-1`
we can substitute `(color(blue)(1+2x))` for `color(red)(y)` to get
`color(white)("XXX")-4x+(color(blue)(1+2x))=-1`

`color(white)("XXX")-2x+1=-1`

`color(white)("XXX")color(green)(x)=color(brown)(1)`

Then substituting `(color(brown)(1))` for `color(green)(x)`
in the original `-2color(green)(x)+y=1`

`color(white)("XXX")-2*(color(brown)(1))+y=1`

`color(white)("XXX")-2+y=1`

`color(white)("XXX")y=3`