# How do solve the following linear system?:  -7x+y=-19 , x-2y=8 ?

May 7, 2017

$\left(\frac{19}{7} , - \frac{37}{14}\right)$

#### Explanation:

From the second equation, by adding $2 y$ to both sides of the equation, we get $x = 2 y + 8$
By substituting this into the first equation, we get $- 7 \left(2 y + 8\right) + y = - 19$
Here we can solve for y:
$- 14 y - 56 + y = - 19$
$- 13 y = 37$
$y = - \frac{37}{13}$
By substituting this value of $y$ into the second equation to find $x$:
$x - 2 \left(- \frac{37}{13}\right) = 8$
$x + \frac{74}{13} = 8$
$x = 8 - \frac{74}{13} = \frac{104 - 74}{13} = \frac{30}{13}$
Thus we get the coordinate point $\left(\frac{30}{13} , - \frac{37}{13}\right)$ as our answer.