# How do you solve the system  6x-2y=2 and 9x-3y=1?

Jun 12, 2015

The given equations represent parallel lines with no intersection point (and therefore no solution).

#### Explanation:

[1]$\textcolor{w h i t e}{\text{XXXX}}$$6 x - 2 y = 2$
$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$$\Rightarrow 3 x - y = 1$
[2]$\textcolor{w h i t e}{\text{XXXX}}$$9 x - 3 y = 1$
$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$$\Rightarrow 3 x - y = \frac{1}{3}$

Since equations [1] and [2] give two different values for $\left(3 x - y\right)$ they represent non-intersecting (parallel) lines.