# How do you solve 6x + y = 23 and x + 5y = 28?

Jun 25, 2016

The solution for the system of equations is :
color(green)(x = 3 , y=5

#### Explanation:

$\textcolor{b l u e}{6 x} + y = 23$...............equation $\left(1\right)$

$x + 5 y = 28$ , multiplying by $6 :$

$\textcolor{b l u e}{6 x} + 30 y = 168$........equation $\left(2\right)$

Subtracting equation $1$ from $2 :$

$\cancel{\textcolor{b l u e}{6 x}} + 30 y = 168$
$- \cancel{\textcolor{b l u e}{6 x}} - y = - 23$

$29 y = 145$

$y = \frac{145}{29}$

color(green)(y = 5

Finding $x$ from equation $2 :$

$x + 5 y = 28$

$x = 28 - 5 y$

$x = 28 - 5 \times 5$

$x = 28 - 25$

color(green)(x = 3