Question

How do you solve -4x+y=-11 and 2x-3y=5?

Answer 1

`(x,y) = (14/5,1/5)`

Explanation:

Given:
[1]`color(white)("XXX")-4x+y=-11`
[2]`color(white)("XXX")2x-3y=5`

Multiply [2] by `2` giving `x` a coefficient of the same magnitude as in [1]
[3]`color(white)("XXX")4x-6y =10`

Add [1] and [3], eliminating the `x` term
[4]`color(white)("XXX")-5y = -1`

Divide both sides of [4] by `(-5)`
[6]`color(white)("XXX")y=1/5`

Multiply [1] by `3` giving `y` a coefficient of the same magnitude as in [2]
[7]`color(white)("XXX")-12x+3y=-33`

Add [2] and [7], eliminating the `y` term
[8]`color(white)("XXX")-10x = -28`

Divide both sides of [8] by `(-10)`
[9]`color(white)("XXX")x=14/5`