# How do solve the following linear system?:  -6x-2y=-8 , 3x – 4y = 7 ?

Apr 26, 2016

The solution for the system of equations is:
color(blue)(x = 23/(15)

color(blue)(y = -3/5

#### Explanation:

$\textcolor{g r e e n}{- 6 x} - 2 y = - 8$ ......equation $\left(1\right)$

$3 x - 4 y = 7$, multiplying by $2$
$\textcolor{g r e e n}{6 x} - 8 y = 14$...............equation $\left(2\right)$

Solving by elimination:

Adding equations $1$ and $2$ eliminates color(green)(6x.

$\cancel{\textcolor{g r e e n}{- 6 x}} - 2 y = - 8$
$\cancel{\textcolor{g r e e n}{6 x}} - 8 y = 14$

$- 10 y = 6$

$y = - \frac{6}{10}$

color(blue)(y = -3/5

Finding $x$ from equation $2$:
$3 x - 4 y = 7$

$3 x = 7 + 4 y$

3x = 7 + 4 * color(blue)((-3/5)

$3 x = 7 - \frac{12}{5}$

$3 x = \frac{35}{5} - \frac{12}{5}$

$3 x = \frac{23}{5}$

$x = \frac{23}{5 \cdot 3}$

color(blue)(x = 23/(15)