# How do solve the following linear system?:  -9x+5y=1 , -x+5y=-13 ?

Nov 26, 2015

$x = - \frac{7}{4}$, $y = - \frac{59}{20}$

#### Explanation:

From the second equation, you have that $x = 5 y + 13$. Substitute this expression for $x$ in the first equation to have

$- 9 \left(5 y + 13\right) + 5 y = 1$. Expand:

$- 45 y - 117 + 5 y = 1$. Isolate the $y$ terms:

$- 40 y = 118$. Solve for $y$:

$y = - \frac{118}{40} = - \frac{59}{20}$.

Once $y$ is known, we can find back $x$:

$x = 5 y + 13 = 5 \cdot \left(- \frac{59}{20}\right) + 13 = - \frac{7}{4}$.