# What are x and y if 10x - 2y = -8 and 3y - 5x = 8?

Oct 21, 2015

#### Answer:

$\left(x , y\right) = \left(- \frac{2}{5} , 2\right)$

#### Explanation:

Given
[1]$\textcolor{w h i t e}{\text{XXX}} 10 x - 2 y = - 8$
[2]$\textcolor{w h i t e}{\text{XXX}} 3 y - 5 x = 8$

Rearrange [2] into standard form order:
[3]$\textcolor{w h i t e}{\text{XXX}} - 5 x + 3 y = 8$

Multiply [3] by $2$ to make coefficients of $x$ in [1] and [4] additive inverses
[4]$\textcolor{w h i t e}{\text{XXX}} - 10 x + 6 y = 16$

Add [1] and [4]
[5]$\textcolor{w h i t e}{\text{XXX}} 4 y = 8$

Divide [5] by $2$
[6]$\textcolor{w h i t e}{\text{XXX}} y = 2$

Substitute $2$ fro $y$ in [1]
[7]$\textcolor{w h i t e}{\text{XXX}} 10 x - 2 \left(2\right) = - 8$

[8]$\textcolor{w h i t e}{\text{XXX}} 10 x - 4 = - 8$

[9]$\textcolor{w h i t e}{\text{XXX}} 10 x = - 4$

[10]$\textcolor{w h i t e}{\text{XXX}} x = - \frac{2}{5}$