# How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent y = 2/3x and y = - 1/3 x + 6?

Apr 20, 2016

$\left(x , y\right) = \left(- 6 , - 4\right)$
This is a consistent system of equations (since it has a single solution)

#### Explanation:

Given:
$\textcolor{w h i t e}{\text{XXX}} y = \frac{2}{3} x$
$\textcolor{w h i t e}{\text{XXX}} y = - \frac{1}{3} x + 6$

Multiplying everything in both equations by $3$
$\textcolor{w h i t e}{\text{XXX}} 3 y = 2 x$
$\textcolor{w h i t e}{\text{XXX}} 3 y = - x + 18$

Subtracting the second from the first:
$\textcolor{w h i t e}{\text{XXX}} 0 = 3 x + 18$
$\textcolor{w h i t e}{\text{XXX}} \Rightarrow x = - 6$

and since $3 y = 2 x$
$\textcolor{w h i t e}{\text{XXX}} 3 y = - 12$
$\textcolor{w h i t e}{\text{XXX}} \Rightarrow y = - 4$