# How do you solve the following system?: 13x -17y =21, -7x -4y = -7

Nov 20, 2015

$\left(\frac{307}{171} , - \frac{238}{171}\right)$

#### Explanation:

Multiply the first equation by 7, and the other by 13.

$7 \cdot \left(13 x - 17 y\right) = 7 \cdot 21$
$91 x - 119 y = 147$

$13 \cdot \left(- 7 x - 4 y\right) = 13 \cdot - 7$
$- 91 x - 52 y = 91$

$91 x - 119 y = 147$
$- 91 x - 52 y = 91$

$91 x - 119 y - 91 x - 52 y = 147 + 91$
$- 171 y = 238$
$y = - \frac{238}{171}$

Now write $- \frac{238}{171}$ instead of $y$ in one of the equations.

$- 7 x + 4 \cdot \frac{238}{171} = - 7$
$x = \frac{307}{171}$