# How do you solve the following system: x-2y=4, 2x-y=7 ?

Mar 15, 2018

$\left(x , y\right) = \left(\frac{10}{3} , - \frac{1}{3}\right)$

#### Explanation:

First, define one variable (let's do x) in terms of the other (y). Using the first equation, we can conclude that $x = 2 y + 4$. Then, we can substitute $2 y + 4$ into anywhere we see x in the second equation, so:
$2 \left(2 y + 4\right) - y = 7$
$4 y + 8 - y = 7$
$3 y + 8 = 7$
$3 y = - 1$
$y = - \frac{1}{3}$
Then, plug y back into the first equation to find x.
$x - 2 \left(- \frac{1}{3}\right) = 4$
$x + \frac{2}{3} = 4$
$x = \frac{10}{3}$