Question

How do you solve `y=x^2-x-20, y=3x+12` using substitution?

Answer 1

`(x,y)=color(green)(""(8,36))` or `color(green)(""(-4,0))`

Explanation:

Given
[1]`color(white)("XXX")y=x^2-x-20`
[2]`color(white)("XXX")y=3x+12`

Using [2] we can substitute `3x+12` for `y` in [1] to get
[3]`color(white)("XXX")3x+12=x^2-x-20`

[4]`color(white)("XXX")rarr x^2-4x-32=0`

[5]`color(white)("XXX")rarr (x-8)(x+4)=0`

[6]`color(white)("XXX")rarr x=8`
or
[7]`color(white)("XXX")rarr x=-4`

Using [6] in [2]
[8]`color(white)("XXX")y=3 * 8 +12 =36` (when `x=8`)
or
Using [7] in [2]
[9]`color(white)("XXX")y=3 * (-4) +12 =0` (when `x=-4`)