# How do you solve the following system?: x +2y = 7 , 2x - 7y = 1

##### 1 Answer
Apr 4, 2018

$\left(x , y\right) = \left(\frac{51}{11} , \frac{13}{11}\right)$

#### Explanation:

$x = 7 - 2 y$ solve for $x$ in terms of $y$ using the first equation
$2 \left(7 - 2 y\right) - 7 y = 1$ plug into the other equation
$14 - 4 y - 7 y = 1$ distribute
$14 - 11 y = 1$ combine
$- 11 y = - 13$
$y = \frac{13}{11}$

Now, going back to the other equation (the first one)
$x + 2 \left(\frac{13}{11}\right) = 7$ plug in value of $y$
$x + \frac{26}{11} = 7$

$x + \frac{26}{11} = \frac{77}{11}$

$x = \frac{51}{11}$