# How do you solve the following system: 3x+4y=-10, x-2y=4 ?

Jan 8, 2016

The solution for the system of equations is
color(blue)(x=-2/5, y=-11/5

#### Explanation:

$\textcolor{b l u e}{3 x} + 4 y = - 10$......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 $1$

$\cancel{\textcolor{b l u e}{3 x}} + 4 y = - 10$
$- \cancel{\textcolor{b l u e}{3 x}} + 6 y = - 12$

$10 y = - 22$

$y = - \frac{22}{10}$

color(blue)(y =-11/5

Finding $x$ from equation $2$
$x - 2 y = 4$

$x = 4 + 2 y$

$x = 4 + 2 \times \left(- \frac{11}{5}\right)$

$x = 4 - \frac{22}{5}$

$x = \frac{20}{5} - \frac{22}{5}$

color(blue)(x= -2/5