How do solve the following linear system?:  2x + 4y = 8 , 2x-y=4 ?

Mar 10, 2016

The solution for the system of equations is:
color(green)(x =12 /5
color(green)(y=4/5

Explanation:

$\textcolor{b l u e}{2 x} + 4 y = 8$...........equation $\left(1\right)$
$\textcolor{b l u e}{2 x} - y = 4$..............equation $\left(2\right)$

Solving by elimination:
Subtracting equation $\left(2\right)$ from $\left(1\right)$ results in elimination of $2 x$:

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

$5 y = 4$

color(green)(y=4/5

Finding $x$ from equation $1$:

$2 x + 4 y = 8$

$2 x = 8 - 4 y$

$2 x = 8 - 4 \times \frac{4}{5}$

$2 x = 8 - \frac{16}{5}$

$2 x = \frac{40}{5} - \frac{16}{5}$

$2 x = \frac{24}{5}$

$x = \frac{\cancel{24}}{5 \times \cancel{2}}$

color(green)(x =12 /5