# How do you solve  1/2x + 1/3y = 5 and 1/4x + y = 10 using substitution?

May 26, 2018

$x = 4 , y = 9$

#### Explanation:

From the second equation we get
$y = 10 - \frac{1}{4} x$
plugging this in the first one
$\frac{1}{2} x + \frac{1}{3} \left(10 - \frac{1}{4} x\right) = 5$
$\frac{1}{2} x + \frac{10}{3} - \frac{1}{12} x = 5$
Multplying by $12$
$6 x + 40 - x = 60$
$5 x = 20$
$x = 4$
so
$y = 9$