# How do solve the following linear system?:  x-3y=-2 , 3x-y=7 ?

Mar 31, 2018

x= 23/8
y=13/8

#### Explanation:

We can just make one of the linear equations in terms of the x and y and then substiute it into the other equation.

$x - 3 y = - 2$

If we rearrange for x we get
$x = - 2 + 3 y$

Then we can substitute this into

$3 x - y = 7$

$3 \left(- 2 + 3 y\right) - y = 7$

$- 6 + 9 y - y = 7$

$8 y = 13$

$y = \frac{13}{8}$

Substitute this into equation one to figure out x

$x = - 2 + 3 \left(\frac{13}{8}\right)$
$x = \frac{23}{8}$