# How do you solve the system of equations: y = 2x ; x + 2y = 8?

Aug 8, 2015

The solution for the system of equations is
color(blue)(x=8/5, y=16/5

#### Explanation:

y=color(blue)(2x......equation $\left(1\right)$
$x + 2 y = 8$....equation $\left(2\right)$

Solving by substitution , substituting equation $1$ in equation $2$

$x + 2 y = 8$

$x + 2 \cdot \textcolor{b l u e}{2 x} = 8$

$x + 4 x = 8$

$5 x = 8$
color(blue)(x=8/5

Substituting the value of $x$ in equation $1$ to find $y$
$y = 2 x$

$y = 2 \cdot \left(\frac{8}{5}\right)$

color(blue)(y=16/5