Question

How do you solve the system `x=-4y` and `3x+2y=20` using substitution?

Answer 1

`(x,y)=(8,-2)`

Explanation:

Given
`color(white)("XXX")color(red)x=color(red)(-4y)`
and
`color(white)("XXX")3color(red)x+2y=20`

Substituting `color(red)(""(-4y))` for `color(red)x` into the second equation:
`color(white)("XXX")3 * color(red)(""(-4y))+2y =20`

`color(white)("XXX")-12 y +2y =20`

`color(white)("XXX")-10y=20`

`color(white)("XXX")color(blue)y=color(blue)(-2)`

Now substitute `color(blue)(""(-2))` for `color(blue)y` back in the original equation `x=-4color(blue)y`

`color(white)("XXX")x=-4 * color(blue)(""(-2))`

`color(white)("XXX")x=8`