Question

How do you solve `x - 2y = 10` and `1/2x - 2y = 4` using substitution?

Answer 1

`(x,y)=color(blue)(12,1)`

Explanation:

Given
[1]`color(white)("XXX")x-2y=10`
[2]`color(white)("XXX")1/2x-2y=4`

We can rearrange [1] to give us an equation in terms of just `x`
[3]`color(white)("XXX")x=2y+10`

This allows us to substitute `(2y+10)` for `x` in [2]
[4]`color(white)("XXX")1/2(2y+10)-2y=4`

Simplifying
[5]`color(white)("XXX")y+5-2y=4`

[6]`color(white)("XXX")-y=-1`

[7]`color(white)("XXX")y=1`

Now we can substitute `1` for `y` back in [1]
[8]`color(white)("XXX")x-2(1)=10`

Simplifying
[9]`color(white)("XXX")x=12`