# How do you solve the system of equations by graphing x+y=3 and x-y=1 and then classify the system?

Jan 13, 2018

This pair of equations are consistent with a single solution
$x = 2$, $y = 1$

#### Explanation:

Graphing solution (sorry I missed this requirement initially.
The graph of $x + y = 3$ looks like:
graph{(3-x) [-10, 10, -5, 5]}
and
the graph of $x - y = 1$ looks like
graph{x-1 [-12.66, 12.65, -6.33, 6.33]}

When combined we have

with a single point of intersection at $\left(x , y\right) = \left(2 , 1\right)$

Non-graphing solution
Given
[1]$\textcolor{w h i t e}{\text{XXX}} x + y = 3$
[2]$\textcolor{w h i t e}{\text{XXX}} x - y = 1$

adding [1] and [2] together gives
[3]$\textcolor{w h i t e}{\text{XXX}} 2 x = 4$
which implies
[4]$\textcolor{w h i t e}{\text{XXX}} x = 2$

subtracting [2] from [1] gives
[5]$\textcolor{w h i t e}{\text{XXX}} 2 y = 2$
which implies
[6]$\textcolor{w h i t e}{\text{XXX}} y = 1$

This pair of equations are consistent with a single solution
$x = 2$, $y = 1$