# How do you solve the following system?:  1/3y = 3/4x + 5 , 3/2x - 8y = 2

Apr 1, 2018

$x = - \frac{244}{33}$ $y = - \frac{18}{11}$

#### Explanation:

$\left(\frac{1}{3}\right) y = \left(\frac{3}{4}\right) x + 5$----(1)
$\left(\frac{3}{2}\right) x - 8 y = 2$----(2)

Multiply (2) by $\left(\frac{1}{2}\right)$
$\left(\frac{3}{4}\right) x - 4 y = 1$----(3)

Add(1)and(3), to make$x$disappear
$\left(\frac{1}{3}\right) y + \left(\frac{3}{4}\right) x - 4 y = \left(\frac{3}{4}\right) x + 5 + 1$
$\left(\frac{3}{4}\right) x - \left(\frac{3}{4}\right) x + \left(\frac{1}{3}\right) y - 4 y = 5 + 1$
$\left(- \frac{11}{3}\right) y = 6$
$y = 6 \cdot \left(- \frac{3}{11}\right)$
$y = - \frac{18}{11}$

Substitude$y = - \frac{18}{11}$into(3)
$\left(\frac{3}{4}\right) x - 4 \left(- \frac{18}{11}\right) = 1$
$\left(\frac{3}{4}\right) x + \frac{72}{11} = 1$
$\left(\frac{3}{4}\right) x = 1 - \frac{72}{11}$
$\left(\frac{3}{4}\right) x = - \left(\frac{61}{11}\right)$
$x = - \left(\frac{61}{11}\right) \cdot \left(\frac{4}{3}\right)$
$x = - \frac{244}{33}$

So, $x = - \frac{244}{33}$ $y = - \frac{18}{11}$