Question

How do you solve the following system: `4x+3y= -1 , x-y=3`?

Answer 1

`x=8/7" or " 1 1/7color(white)("xxxx")y=-13/7" or " -1 6/7`

Explanation:

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

Re-arranging [2]
[3]`color(white)("XXX")x=y+3`

Substituting `(y+3)` for `x` in [1]
[4]`color(white)("XXX")4(y+3)+3y=-1`

Expanding and simplifying the lefts side of [4]
[5]`color(white)("XXX")7y+12=-1`

Subtracting `12` from both sides of [5]
[6]`color(white)("XXX")7y=-13`

Dividing both sides of [6] by 7
[8]`color(white)("XXX")y=-13/7`

Substituting `(-13/7)` for `y` in [3]
[9]`color(white)("XXX")x=-13/7+3=(-13+21)/7=8/7`