# How do you solve the following system?: 5x-7y=22 , 4x-3y=15

Nov 26, 2017

$x = 3$ and $y = - 1$

#### Explanation:

$7 \cdot \left(4 x - 3 y\right) - 3 \cdot \left(5 x - 7 y\right) = 15 \cdot 7 - 3 \cdot 22$

$\left(28 x - 21 y\right) - \left(15 x - 21 y\right) = 105 - 66$

$13 x = 39$, so $x = 3$

$5 \cdot 3 - 7 y = 22$

$15 - 7 y = 22$

$- 7 y = 7$, so $y = - 1$