# How do you solve the system 5x + y = 13 & 2x + 6y =22?

Jan 30, 2017

$\text{the answer is x=2 and y=3}$

#### Explanation:

$5 x + y = 13 \text{ (1)}$
$2 x + 6 y = 22 \text{ (2)}$

$\text{let us multiply the both sides of equation (1) by 6}$
$\textcolor{red}{6.} \left(5 x + y\right) = \textcolor{red}{6.} 13$
$30 x + 6 y = 78 \text{ (3)}$

$\text{subtract equation (2) from equation (3)}$
$30 x + 6 y - \left(2 x + 6 y\right) = 78 - 22$
$30 x \cancel{+ 6 y} - 2 x \cancel{- 6 y} = 56$
$28 x = 56$

$x = \frac{56}{28}$

color(green)(x=2);

$\text{now use (1) or (2)}$

$5 . \textcolor{g r e e n}{2} + y = 13$
$10 + y = 13$

$y = 13 - 10$

$y = 3$