# How do you solve the following system: 4x-2y=4 , 4x-5y-23=0 ?

Jun 14, 2017

$x = - \frac{13}{6} \mathmr{and} y = - \frac{19}{3}$

#### Explanation:

Write both equations with $4 x$ as the subject.

$4 x = 2 y + 4 \text{ and } 4 x = 5 y + 23$

$\textcolor{w h i t e}{\times \times \times \times} 4 x = 4 x$

$\textcolor{w h i t e}{\times \times x} 5 y + 23 = 2 y + 4$

$\textcolor{w h i t e}{\times \times x} 5 y - 2 y = 4 - 23$

$\textcolor{w h i t e}{\times \times \times \times} 3 y = - 19$

$\textcolor{w h i t e}{\times \times \times \times x} y = - \frac{19}{3}$
$4 x = \left(2 y + 4\right)$

$x = \frac{2 y + 4}{4}$

$x = \left(2 \left(\frac{- 19}{3}\right) + 4\right) \div 4$

$x = - \frac{13}{6}$

Check:

$4 x = 5 y + 23$

$4 \times \frac{- 13}{6} = 5 \left(\frac{- 19}{3}\right) + 23$

$- \frac{26}{3} = - \frac{26}{3}$