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

Jul 1, 2015

The point of intersection occurs at $\left(x , y\right) = \left(6 , 2\right)$

#### Explanation:

[1]$\textcolor{w h i t e}{\text{XXXX}}$$x + 3 y = 12$
[2]$\textcolor{w h i t e}{\text{XXXX}}$$x - y = 4$

Subtract [2] from [1] to remove the variable $x$ from the equation
[3]$\textcolor{w h i t e}{\text{XXXX}}$4y = 8#

Divide both sides of [3] by $4$
[4]$\textcolor{w h i t e}{\text{XXXX}}$$y = 2$

Substitute $y = 2$ in [1]
[5]$\textcolor{w h i t e}{\text{XXXX}}$$x + 3 \left(2\right) = 12$

Simplifying
[6]$\textcolor{w h i t e}{\text{XXXX}}$$x = 6$