Question

How do you solve the following system using substitution?: #x-3y=2, x+y=-10#

Answer 1

`(x,y) = (-7,-3)`

Explanation:

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

Rearrange [1], isolating `x` on one side:
[3]`color(white)("XXX")x=3y+2`

Substitute `(3y+2)` for `x` in [2]
[4]`color(white)("XXX")(3y+2)+y=-10`

Simplify
[5]`color(white)("XXX")4y=-12`

[6]`color(white)("XXX")y=-3`

Substitute `(-3)` for `y` in [1]
[7]`color(white)("XXX")x-3(-3) = 2`

[8]`color(white)("XXX")x+9 = 2`

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