# How do you solve the following system: 2x + y = 8 , x-10y=10 ?

Jan 15, 2016

The solution is
color(blue)(x = 30/7
color(blue)(y = -4/7

#### Explanation:

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

$x - 10 y = 10$, multiplying by $2$
$\textcolor{b l u e}{2 x} - 20 y = 20$....equation $\left(2\right)$

Solving by elimination:
Subtracting equation $2$ from $1$

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

$21 y = - 12$

$y = - \frac{12}{21}$

color(blue)(y = -4/7

Finding $x$ from equation $2$:
$x - 10 y = 10$

$x = 10 + 10 y$

$x = 10 + 10 \times - \frac{4}{7}$

$x = 10 - \frac{40}{7}$

$x = \frac{70}{7} - \frac{40}{7}$

color(blue)(x = 30/7