# How do you solve the following system:  8x-7y=-39, 7x-2y= -67 ?

Jul 5, 2017

By arranging equations. $x = - \frac{391}{33}$ and $y = - \frac{263}{33}$

#### Explanation:

Multiply the first equation by $- 2$ and the second by $7$:

$- 16 x + 14 y = 78$
$49 x - 14 y = - 469$

Add these equations (provided above), yielding

$49 x - 16 x = - 391$

$33 x = - 391$

$x = - \frac{391}{33}$

When you put this value for $x$ (for instance in the first original equation), you will find $y$.

$8 \times \left(- \frac{391}{33}\right) - 7 y = - 39$

$- 7 y = - 39 + \frac{3128}{33}$

$- 7 y = \frac{- 1287 + 3128}{33}$

$- 7 y = \frac{1841}{33}$

$y = - \frac{1841}{231}$

$y = - \frac{263}{33}$