Question

How do you solve the system of equations `x+5y-10=0` and `x=2y-8` using substitution?

Answer 1

`(x,y)=color(green)(""(-20/7,18/7))`
(see below for solution using substitution)

Explanation:

Given
[1]`color(white)("XXX")x+5y-10=0`
[2]`color(white)("XXX")x=2y-8`

Substituting (from [2]) `2y-8` or `x` in [1]
[3]`color(white)("XXX")2y-8+5y-10=0`

[4]`color(white)("XXX")7y-18=0`

[5]`color(white)("XXX")=18/7`

Substituting `18/7` for `y` in [2]
[6]`color(white)("XXX")x=2(18/7)-8`

[7]`color(white)("XXX")x=-20/7`