# How do you find the point of intersection for x+y=3 and 2x-y= -3?

Jun 26, 2015

The given lines intersect at $\left(0 , 3\right)$

#### Explanation:

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

[3]$\textcolor{w h i t e}{\text{XXXX}}$$3 x = 0$
[4]$\textcolor{w h i t e}{\text{XXXX}}$$x = 0$

substituting $0$ for $x$ in [1]
$\textcolor{w h i t e}{\text{XXXX}}$$0 + y = 3$
$\textcolor{w h i t e}{\text{XXXX}}$$y = 3$

Jun 26, 2015

I found the point of intersection of coordinates:
$x = 0$
$y = 3$

#### Explanation:

You basically solve the System of the two equations trying to find values of $x$ and $y$ that satisfy both equations simultaneously.
From the first you can isolate $x$ as:
$x = 3 - y$
now you can substitute this $x$ into the second equation and find $y$ as:
$2 \left(3 - y\right) - y = - 3$
$6 - 2 y - y = - 3$
$- 3 y = - 9$
$y = 3$
substitute back this value into the first equation to find $x$:
$x = 3 - 3 = 0$