Question

How do you solve `2x+3y=6` and `y=2x-6` using substitution?

Answer 1

`(x,y)=color(blue)(""(3,0))`
(see below for solution by substitution)

Explanation:

Given
[1]`color(white)("XXX")2x+3y=6`
[2]`color(white)("XXX")y=2x-6`

Since from [2] we have that `y=2x-6`
we can replace `y` with `(2x-6)` in [1]
to get
[3]`color(white)("XXX")2x+3(2x-6)=6`

Simplifying
[4]`color(white)("XXX")8x-18=6`

[5]`color(white)("XXX")rarr 8x=24`

[6]`color(white)("XXX")rarr x=3`

Since from [6] `x=3`
we can replace `x` with `(3)` in [2]
to get
[7]`color(white)("XXX")y=2(3)-6`

and simplifying
[8]`color(white)("XXX")y=0`