# How do you solve 3x+4y=0 and x-4y= -8?

Mar 5, 2018

$x = - 2$ and $y = \frac{3}{2}$

#### Explanation:

Given
[1]$\textcolor{w h i t e}{\text{XXX}} 3 x + 4 y = 0$
[2]$\textcolor{w h i t e}{\text{XXX}} x - 4 y = - 8$

Adding equations [1] and [2] together
[3]$\textcolor{w h i t e}{\text{XXX}} 4 x = - 8$

Dividing both sides of [3] by $4$
[4]$\textcolor{w h i t e}{\text{XXX}} x = - 2$

Substituting $\left(- 2\right)$ for $x$ back in [2]
[5]$\textcolor{w h i t e}{\text{XXX}} \left(- 2\right) - 4 y = - 8$

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

$r a r$r[7]$\textcolor{w h i t e}{\text{XXX}} y = \frac{3}{2}$ ...or if you prefer a mixed number $y = 1 \frac{1}{2}$