# How do you solve -x + 2y = 6 and x + 4y =24?

Mar 14, 2016

The solution for the system of equations is:
color(blue)(x=4
color(blue)(y=5

#### Explanation:

$\textcolor{b l u e}{- x} + 2 y = 6$ ..............equation $\left(1\right)$
$\textcolor{b l u e}{x} + 4 y = 24$.................equation $\left(2\right)$

Solving by elimination.

Adding equations $1$ and $2$ results in elimination of $\textcolor{b l u e}{x}$

$\cancel{\textcolor{b l u e}{- x}} + 2 y = 6$
$\cancel{\textcolor{b l u e}{x}} + 4 y = 24$

$6 y = 30$

$y = \frac{30}{6}$

color(blue)(y=5

Finding $x$ from equation $\left(1\right)$:
$- x + 2 y = 6$

$2 y - 6 = x$

$2 \cdot \textcolor{b l u e}{5} - 6 = x$

$10 - 6 = x$

color(blue)(x=4