Question

How do you find the point of intersection for `x+3y=12` and `x-y=4`?

Answer 1

The point of intersection occurs at `(x,y) = (6,2)`

Explanation:

[1]`color(white)("XXXX")` `x+3y=12`
[2]`color(white)("XXXX")` `x-y = 4`

Subtract [2] from [1] to remove the variable `x` from the equation
[3]`color(white)("XXXX")`4y = 8#

Divide both sides of [3] by `4`
[4]`color(white)("XXXX")` `y = 2`

Substitute `y=2` in [1]
[5]`color(white)("XXXX")` `x+3(2) = 12`

Simplifying
[6]`color(white)("XXXX")` `x = 6`