# How do you find the point of intersection for 3x-y=1 and x+y=3?

Jul 31, 2015

$\left(x , y\right) = \left(1 , 2\right)$

#### Explanation:

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

[3]$\textcolor{w h i t e}{\text{XXXX}}$$4 x = 4$
[4]$\textcolor{w h i t e}{\text{XXXX}}$$x = 1$
Substitute $1$ for $x$ in [2]
[5]$\textcolor{w h i t e}{\text{XXXX}}$$1 + y = 3$
Subtract $1$ from both sides of [5]
[6]$\textcolor{w h i t e}{\text{XXXX}}$$y = 2$