Question

How do you solve `8x+5y=-4` and `-5x+y=19` using substitution?

Answer 1

`(x,y)=color(blue)(""(-3,4))`
(see below for solution using substitution).

Explanation:

Given
[1]`color(white)("XXX")8x+5y=-4`
[2]`color(white)("XXX")-5x+y=19`

Note that [2] can be re-written as
[3]`color(white)("XXX")y=5x+19`

We can therefore substitute `(5x+19)` in place of `y` in [1]
[4]`color(white)("XXX")8x+5(5x+19)=-4`

[5]`color(white)("XXX")33x+95=-4`

[6]`color(white)("XXX")33x=-99`

[7]`color(white)("XXX")x=-3`

We can now substitute `(-3)` in place of `x` in [3]
[8]`color(white)("XXX")y=5(-3)+19`

[9]`color(white)("XXX")y=4`