Question

How do you solve `9x - y = 317` and `10x - 11y = 550` using substitution?

Answer 1

`(x,y)=color(green)(""(33,-20))`
(see below for solution by substitution)

Explanation:

Given
[1]`color(white)("XXX")9x-y=317`
[2]`color(white)("XXX")10x-11y=550`

We can re-arrange [1] as
[3]`color(white)("XXX")y=9x-317`

Using [3] we can substitute `9x-317` for `y` in [2]
[4]`color(white)("XXX")10x-11(9x-317)=550`

[5]`color(white)("XXX")10x-99x=550-3487`

[6]`color(white)("XXX")89x=2937`

[7]`color(white)("XXX")x=33`

Using [7] we can substitute `33` for `x` in [1]
[8]`color(white)("XXX")9(33)-y=317`

[9]`color(white)("XXX")297-y=317`

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