# How do you solve the following system?:  x + 6y = 13 , 5y = x + 10

Mar 11, 2018

$x = \frac{5}{11} , y = \frac{23}{11}$

#### Explanation:

$x + 6 y = 13$ Eqn (1)

$5 y = x + 10$

$- x + 5 y = 10$ Eqn (2). Rearranging variables to L H S.

Adding Eqns (1), (2),

$6 y + 5 y = 23$ , $11 y = 23$

$y = \frac{23}{11}$

Substituting value of y in Eqn (1),

$x + 6 \cdot \left(\frac{23}{11}\right) = 13$

$11 x + 138 = 143$

$11 x = - 138 + 143 = 5$

$x = \frac{5}{11}$