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

Dec 6, 2015

The solution for the system of equations is
color(blue)(x=-9/7 , y=-19/7

#### Explanation:

$\textcolor{b l u e}{3 x} - 4 y = 7$.........equation $\left(1\right)$

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

Solving by elimination

Subtracting equation $2$ from $1$ results in elimination of color(blue)(3x

$\cancel{\textcolor{b l u e}{3 x}} - 4 y = 7$
$- \cancel{\textcolor{b l u e}{3 x}} - 3 y = + 12$

$- 7 y = 19$

$y = \frac{19}{- 7}$

color(blue)(y=-19/(7)

Finding $x$ by substituting $y$ in equation $2$:
$x + y = - 4$

$x = - 4 - y$

$x = - 4 - \left(- \frac{19}{7}\right)$

$x = - 4 + \frac{19}{7}$

$x = - \frac{28}{7} + \frac{19}{7}$

color(blue)(x=-9/7