# How do you solve the following system?: -2x -5y =13, 3x -6y = -4

May 20, 2018

$x = - \frac{98}{27}$ and $y = - \frac{31}{27}$

#### Explanation:

$3 \cdot \left(- 2 x - 5 y\right) + 2 \cdot \left(3 x - 6 y\right) = 3 \cdot 13 + 2 \cdot \left(- 4\right)$

$- 6 x - 15 y + 6 x - 12 y = 39 - 8$

$- 27 y = 31$, so $y = \frac{31}{- 27} = - \frac{31}{27}$

Thus,

$- 2 x - 5 \cdot \left(- \frac{31}{27}\right) = 13$

$- 2 x + \frac{155}{27} = 13$

$- 2 x = \frac{196}{27}$ or $x = \frac{\frac{196}{17}}{- 2} = - \frac{98}{27}$