Question

How do you solve `8x = -2y - 10` and `2x = 4y` using substitution?

Answer 1

`(x,y)=color(blue)(""(-10/9,-5/9))`

Explanation:

Given:
[1]`color(white)("XXX")8x=-2y-10`
[2]`color(white)("XXX")2x=4y`

Dividing both sides of [2] by 2
[3]`color(white)("XXX")x=2y`

From [3] we see that we can substitute `2y` anywhere for `x`
and specifically we can substitute `2y` for `x` in [1] to get
[4]`color(white)("XXX")8(2y)=-2y-10`

Simplifying:
[5]`color(white)("XXX")16y=-2y-10`

[6]`color(white)("XXX")18y=-10`

[7]`color(white)("XXX")y=-5/9`

We can now substitute `(-5/9)` for `y` in [3] to get
[8]`color(white)("XXX")x=2(-5/9)=-10/9`