# Question #02b23

Mar 29, 2017

$\left(x , y\right) = \left(- \frac{4}{3} , \frac{2}{3}\right)$

#### Explanation:

I've no idea what the leading $\left(- 3 , 1\right)$ means.

Since this was asked under the heading "Systems Using Substitution", I will demonstrate how to solve the given two equations (using substitution.

Given
[1]$\textcolor{w h i t e}{\text{XXX}} x - y = - 2$
[2]$\textcolor{w h i t e}{\text{XXX}} x + 5 y = 2$

Rewriting [1] as a definition in terms of $x$
[3]$\textcolor{w h i t e}{\text{XXX}} x = y - 2$

We can now substitute $y - 2$ for $x$ in equation [2]
[4]$\textcolor{w h i t e}{\text{XXX}} \left(y - 2\right) + 5 y = 2$

$\rightarrow$[5]$\textcolor{w h i t e}{\text{XXX}} 6 y = 4$

$\rightarrow$[6]$\textcolor{w h i t e}{\text{XXX}} y = \frac{2}{3}$

Now substitute $\frac{2}{3}$ for $y$ in [1]
[7]$\textcolor{w h i t e}{\text{XXX}} x - \frac{2}{3} = - 2$

$\rightarrow$[8]$\textcolor{w h i t e}{\text{XXX}} x = - \frac{6}{3} + \frac{2}{3} = - \frac{4}{3}$