# How do solve the following linear system?:  4 x+ 6y = 2 , -2x -8y = 4 ?

Feb 24, 2016

The solution is:

color(blue)(x=2
color(blue)(y=-1

#### Explanation:

$\textcolor{b l u e}{4 x} + 6 y = 2$.........equation $1$

$- 2 x - 8 y = 4$, multiplying by $2$
$\textcolor{b l u e}{- 4 x} - 16 y = 8$.....equation $2$

Solving by elimination:
$\cancel{\textcolor{b l u e}{4 x}} + 6 y = 2$
$\cancel{\textcolor{b l u e}{- 4 x}} - 16 y = 8$

$- 10 y = 10$

$y = \frac{10}{- 10}$

color(blue)(y=-1

Finding $x$ from equation $1$:
$4 x + 6 y = 2$

$4 x + 6 \times - 1 = 2$

$4 x - 6 = 2$

$4 x = 2 + 6$

$4 x = 8$

$x = \frac{8}{4}$

color(blue)(x=2