# How do you solve the system of equations: x + y = 6, and y = 2x?

Aug 8, 2015

The solution for the system of equations is
color(green)(x=2, y=4

#### Explanation:

$x + y = 6$.....equation $\left(1\right)$

y=color(green)(2x..........equation $\left(2\right)$

Solving through substitution
Substituting equation $\left(2\right)$ in $\left(1\right)$:

$x + y = 6$

$x + \textcolor{g r e e n}{2 x} = 6$

$3 x = 6$
color(green)(x=2

Now substituting $x$ in equation $2$ to find $y$

$y = 2 x$
$y = 2 \cdot 2$
color(green)(y=4