# How do you solve the following system: -2x + 5y = 20, 2x – 4y = 8?

Dec 26, 2015

The solution for the system of equations is

color(blue)(x=60, y=28

#### Explanation:

$\textcolor{b l u e}{- 2 x} + 5 y = 20$.......equation $\left(1\right)$

$\textcolor{b l u e}{2 x} - 4 y = 8$.............equation $\left(2\right)$

Solving by elimination.
Adding equations $1$ and $2$

$\cancel{\textcolor{b l u e}{- 2 x}} + 5 y = 20$
$\cancel{\textcolor{b l u e}{2 x}} - 4 y = 8$

color(blue)(y=28

Finding $x$ by substituting $y$ in equation $1$

$- 2 x + 5 y = 20$

$- 2 x + 5 \times \textcolor{b l u e}{28} = 20$

$- 2 x + 140 = 20$

$- 2 x = 20 - 140$

$- 2 x = - 120$

$x = \frac{120}{2}$

color(blue)(x=60