Question

How do you solve the following linear system `4x - y = 5 , 4x + 4y = -4`?

Answer 1

`(x,y) = (4/5,-9/5)`

Explanation:

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

Subtract [2] from [1]
[3]`color(white)("XXX")-5y= 9`

Divide [3] by `(-5)`
[4]`color(white)("XXX")y= -9/5`

Divide [2] by `4`
[5]`color(white)("XXX")x+y=-1`

Substitute `(-9/5)` from [4] for `y` in [5]
[6]`color(white)("XXX")x-9/5= -1`

Add `9/5` to both sides of [6]
[7]`color(white)("XXX")x=4/5`