# How do you find the point of intersection for x-y=4 and x-3y= -6?

Jun 28, 2015

$x - y = 4$ and $x - 3 y = - 6$ intersect at $\left(x , y\right) = \left(9 , 5\right)$

#### Explanation:

[1]$\textcolor{w h i t e}{\text{XXXX}}$$x - y = 4$
[2]$\textcolor{w h i t e}{\text{XXXX}}$$x - 3 y = - 6$

Subtract [2] from [1]
[3]$\textcolor{w h i t e}{\text{XXXX}}$$2 y = 10$

Divide both sides by 2
[4]$\textcolor{w h i t e}{\text{XXXX}}$$y = 5$

Substitute $5$ for $y$ back in [1] (we could have used either [1] or [2])
[5]$\textcolor{w h i t e}{\text{XXXX}}$$x - 5 = 4$

[6]$\textcolor{w h i t e}{\text{XXXX}}$$x = 9$