# How do you solve the following linear system: x-6y= 7 , 5x+2y=10 ?

Dec 2, 2015

$x = \frac{37}{16}$, $y = - \frac{25}{32}$

#### Explanation:

From the first equation, you have that $x = 6 y + 7$. Substitute this expression for $x$ in the second equation to have

$5 \left(6 y + 7\right) + 2 y = 10$

$30 y + 35 + 2 y = 10$

$32 y = - 25$

$y = - \frac{25}{32}$

Once $y$ is known, you can get $x$ from

$x = 6 y + 7 = 6 \cdot \left(- \frac{25}{32}\right) + 7 = \frac{37}{16}$