Question

How do you solve the following linear system: `-2x+5y=4, 4x+5y=-2`?

Answer 1

`(x,y)=(-1,2/5)`

Explanation:

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

Subtract [1] from [2]
[3]`color(white)("XXX")6x=-6`

Divide both sides of [3] by `6`
[4]`color(white)("XXX"color(green)(x=-1)`

Substitute `(-1)` from [4] for `x` in [1]
[5]`color(white)("XXX")-2xx(-1)+5y=4`

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

Divide both sides of [6] by `5`
[7]`color(white)("XXX")color(green)(y=2/5)`