# How do you solve the following system?:  -2x +5y =-6 , 5x +6y = -1

Jul 11, 2016

$x = \frac{31}{37} , y = - \frac{32}{37}$

#### Explanation:

We can solve for $y$ first by multiplying the first equation by $5$ and the second equation by $2$:

$5 \left(- 2 x + 5 y\right) = \left(- 6\right) 5$ and $2 \left(5 x + 6 y\right) = \left(- 1\right) 2$

Then we add the two equations, resulting in:

$25 y + 12 y = - 32$, and therefore, $37 y = - 32$

We divide both sides by $37$, so $y = - \frac{32}{37}$

To solve for $x$, we multiply the first equation by $- 6$ and the second equation by $5$:

$- 6 \left(- 2 x + 5 y\right) = - 6 \left(- 6\right)$ and $5 \left(5 x + 6 y\right) = 5 \left(- 1\right)$

Then we add the two equations, resulting in:

$12 x + 25 x = 31$, and therefore, $37 x = 31$

We divide both sides by $37$, so $x = \frac{31}{37}$

You can verify these answers by substituting $\frac{31}{37}$ for $x$ and $- \frac{32}{37}$ for $y$:

$- 2 \left(\frac{31}{37}\right) + 5 \left(- \frac{32}{37}\right) = - \frac{62}{37} - \frac{160}{37} = - \frac{222}{37} = - 6$