# How do you solve 4x + 2y = 12 and x + 2y = 6?

May 2, 2016

The solution for the system of equations is:
color(blue)(x =2
color(blue)(y = 2

#### Explanation:

$4 x + \textcolor{b l u e}{2 y} = 12$........equation $\left(1\right)$
$x + \textcolor{b l u e}{2 y} = 6$..............equation $\left(2\right)$

Solving by elimination:

Subtracting equation $2$ from $1$ eliminates color(blue)(2y

$4 x + \cancel{\textcolor{b l u e}{2 y}} = 12$
$- x - \cancel{\textcolor{b l u e}{2 y}} = - 6$

$3 x = 6$

$x = \frac{6}{3}$

color(blue)(x =2

Finding $y$ from equation $1$:
$4 x + 2 y = 12$

$2 y = 12 - 4 x$

2y = 12 - 4 * color(blue)(2

$2 y = 12 - 8$

$2 y = 4$

$y = \frac{4}{2}$

color(blue)(y = 2