# How do you solve the following system?: -12x -15y =3, 13x -16y = -4

Jul 24, 2017

After some arrangement, $x = - 12$ and $y = \frac{1}{43}$

#### Explanation:

Enlarge the first equation with 13 and the second equation with 12:

$- 156 x - 195 y = 39$
$156 x - 192 y = - 48$

Combine these two equations:

$- 387 y = - 9$

$y = \frac{9}{387}$

$y = \frac{1}{43}$

Now you can calculate x (for example using the second original equation):

$13 x - \frac{16}{43} = - 4$

$13 x = - 4 + \frac{16}{43}$

$13 x = - 156$

$x = - \frac{156}{13}$

$x = - 12$