# How do you solve the following system?:  -9x - 3y = 2 , 3x – y = -1

Dec 23, 2016

$\textcolor{g r e e n}{x = - \frac{5}{18} , y = \frac{1}{6}}$

#### Explanation:

Given
[1]$\textcolor{w h i t e}{\text{XXX}} - 9 x - 3 y = 2$
[2]$\textcolor{w h i t e}{\text{XXX}} 3 x - y = - 1$

Multiplying [2] by $3$
$\textcolor{w h i t e}{\text{XXXX}} 3 \times \left(3 x - y\right) = 3 \times \left(- 1\right)$
[3]$\textcolor{w h i t e}{\text{XXX}} 9 x - 3 y = - 3$

$\textcolor{w h i t e}{\text{XXXX}} - 9 x - 3 y = 2$
$\textcolor{w h i t e}{\text{XXXXX}} \underline{9 x - 3 y} = \underline{- 3}$
[4]$\textcolor{w h i t e}{\text{XXXXXX}} - 6 y = - 1$

Dividing [4] by $\left(- 6\right)$
$\textcolor{w h i t e}{\text{XXX}} \frac{\cancel{- 6} y}{\cancel{- 6}} = \frac{\cancel{-} 1}{\cancel{-} 6}$
[5]$\textcolor{w h i t e}{\text{XXX}} y = \frac{1}{6}$

Substituting $\left(\frac{1}{6}\right)$ for $y$ in [2]
[6]$\textcolor{w h i t e}{\text{XXX}} 3 x - \left(\frac{1}{6}\right) = - 1$

Adding $\frac{1}{6}$ to both sides of [6]
$\textcolor{w h i t e}{\text{XXX}} 3 x \cancel{- \left(\frac{1}{6}\right)} \cancel{+ \frac{1}{6}} = - 1 + \frac{1}{6}$

[7]$\textcolor{w h i t e}{\text{XXX}} 3 x = - \frac{5}{6}$

Dividing both sides of [7] by $3$
$\textcolor{w h i t e}{\text{XXX}} \frac{\cancel{3} x}{\cancel{3}} = - \frac{\frac{5}{6}}{3}$

[8]$\textcolor{w h i t e}{\text{XXX}} x = - \frac{5}{18}$