Question

How do you solve the following linear system: #-4x-5y=13 , 2x+3y=-7 #?

Answer 1

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

Explanation:

Given:
[1]`color(white)("XXX")-4x-5y=13`
[2]`color(white)("XXX")2x+3y=-7`

Multiply [2] by `2` to give `x` a coefficient with the same magnitude as in [1]
[3]`color(white)("XXX")4x+6y=-14`

Add [1] and [3] to eliminate the `x` term
[4]`color(white)("XXX")y=-1`

Substitute `(-1)` for `y` in [1]
[5]`color(white)("XXX")-4x-5xx(-1) = 13`

Simplify
[6]`color(white)("XXX")-4x+5=13`

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

[8]`color(white)("XXX")x=-2`