Question

What are x and y if `10x - 2y = -8` and `3y - 5x = 8`?

Answer 1

`(x,y) = (-2/5,2)`

Explanation:

Given
[1]`color(white)("XXX")10x-2y = -8`
[2]`color(white)("XXX")3y-5x=8`

Rearrange [2] into standard form order:
[3]`color(white)("XXX")-5x+3y=8`

Multiply [3] by `2` to make coefficients of `x` in [1] and [4] additive inverses
[4]`color(white)("XXX")-10x+6y = 16`

Add [1] and [4]
[5]`color(white)("XXX")4y=8`

Divide [5] by `2`
[6]`color(white)("XXX")y=2`

Substitute `2` fro `y` in [1]
[7]`color(white)("XXX")10x-2(2)=-8`

[8]`color(white)("XXX")10x -4 = -8`

[9]`color(white)("XXX")10x = -4`

[10]`color(white)("XXX")x=-2/5`