# How do solve the following linear system?:  x - 3y = 8 , 8x+2y=2 ?

May 13, 2017

$x = \frac{11}{13} , y = - \left(\frac{31}{13}\right)$

#### Explanation:

We can solve this using elimination of variables. We can multiply$x - 3 y = 8$ by $8$ to get $8 x - 24 y = 64$. We can then subtract the two equations:

$\left(8 x + 2 y = 2\right) - \left(8 x - 24 y = 64\right) \implies 26 y = - 62$

Dividing both sides of the equation by 26, we get:

$y = - \left(\frac{62}{26}\right) \implies y = - \left(\frac{31}{13}\right)$

Substituting the value of $y$ into the first equation, we get:

$x - 3 \left(- \left(\frac{31}{13}\right)\right) = 8 \implies x + \frac{93}{13} = 8$

$x = 8 - \frac{93}{13} \implies x = \frac{104}{13} - \frac{93}{13}$

$x = \frac{11}{13}$