# How do you solve the following system: 3x+y=8, x-2y=4 ?

Jan 18, 2016

The solution for the system of equations is
color(blue)(x=20/7 , y=-4/7

#### Explanation:

$\textcolor{b l u e}{3 x} + y = 8$........equation $\left(1\right)$

$x - 2 y = 4$, multiplying by $3$
$\textcolor{b l u e}{3 x} - 6 y = 12$.....equation $\left(2\right)$

Solving by elimination.

Subtracting equation $2$ from $1$:
$\cancel{\textcolor{b l u e}{3 x}} + y = 8$
$- \cancel{\textcolor{b l u e}{3 x}} + 6 y = - 12$

$7 y = - 4$
color(blue)(y=-4/7

Finding $x$ from equation $2$

$x - 2 y = 4$

$x = 4 + 2 y$

$x = 4 + 2 \times \left(- \frac{4}{7}\right)$

$x = 4 + \left(- \frac{8}{7}\right)$

$x = \frac{28}{7} + \left(- \frac{8}{7}\right)$

color(blue)(x=20/7