Question

How do you solve the following system?: `-x-8y=32, y= 1/2x +2`

Answer 1

`(x,y)=(-48/5,-14/5)`

Explanation:

[1]`color(white)("XXX")-x-8y=32`
[2]`color(white)("XXX")y=1/2x+2`

Substitute `(1/2x+2)` from [2] for `y` in [1]
[3]`color(white)("XXX")-x -8(1/2x+2) = 32`

Simplify
[4]`color(white)("XXX")-x-4x-16 = 32`

[5]`color(white)("XXX")-5x=48`

[6]`color(white)("XXX")x=-48/5`

Substitute `(-48/5)` from [6] for `x` in [2]
[7]`color(white)("XXX")y=1/2(-48/5) + 2`

Simplify
[8]`color(white)("XXX")y=-14/5`