Question

How do you solve the following system?: `-5x - 5y = -6 , 3x – y = -1`

Answer 1

`(x,y)=(1/20,23/20)`

Explanation:

Given:
[1]`color(white)("XXX")-5x-5y=-6`
[2]`color(white)("XXX")3x-y=-1`

Rearrange [2] to isolate the `y` term on the left side:
[3]`color(white)("XXX")-y=-1-3x`

(the next two steps are not necessary, but I find it easier to work with positives)
Multiply both [1] and [3] by `(-1)` to reverse the signs
[4]`color(white)("XXX")5x+5y=6`
[5]`color(white)("XXX")y=1+3x`

Substitute `(1+3x)` from [5] for `y` in [4]
[6]`color(white)("XXX")5x+5(1+3x)=6`

Simplify [6]
[7]`color(white)("XXX")20x+5=6`

Subtract `5` from both sides of [7]
[8]`color(white)("XXX")20x=1`

Divide both sides of [8] by `20`
[9]`color(white)("XXX")color(green)(x=1/20)`

Substitute `1/20` from [9] for `x` in [2]
[10]`color(white)("XXX")3xx1/20-y=-1`

Subtract `(3/20)` from both sides of [10]
[11]`color(white)("XXX")-y=-23/20`

Multiply both sides of [11] by `(-1)`
[12]`color(white)("XXX")color(green)(y=23/20)`