# How do you solve the following system?: 5x + 2y =1 ,3x-7y=-12

Mar 6, 2016

$x = - \frac{17}{41}$

$y = \frac{63}{41}$

#### Explanation:

$5 \cdot x + 2 \cdot y = 1$

$3 \cdot x - 7 \cdot y = - 12$

Multiply the first equation by $3.5$

$17.5 \cdot x + 7 \cdot y = 3.5$

$3 \cdot x - 7 \cdot y = - 12$

Add the two equations to get

$20.5 \cdot x + \cancel{7 y} - \cancel{7 y} = - 8.5$

$x = - \frac{8.5}{20.5} = - \frac{17}{41}$

This means that you have

$3 \cdot \left(- \frac{17}{41}\right) - 7 y = - 12$

$y = \frac{12 - 3 \cdot \frac{17}{41}}{7} = \frac{63}{41}$