# How do you solve the following system: 4x+3y= -7, y + 4x = 16 ?

Feb 14, 2016

The solution for the system of equations is:
color(blue)(x=55/8

color(blue)(y=-23/2

#### Explanation:

$\textcolor{b l u e}{4 x} + 3 y = - 7$..........equation $1$

$\textcolor{b l u e}{4 x} + y = 16$.................equation $2$

Solving by elimination

Subtracting equation $2$ from $1$
$\cancel{\textcolor{b l u e}{4 x}} + 3 y = - 7$

$- \cancel{\textcolor{b l u e}{4 x}} - y = - 16$

$2 y = - 23$

color(blue)(y=-23/2

Finding $x$ from equation $1$

$4 x + 3 y = - 7$

$4 x + 3 \times \left(- \frac{23}{2}\right) = - 7$

$4 x - \frac{69}{2} = - 7$

$4 x = - 7 + \frac{69}{2}$

$4 x = - \frac{14}{2} + \frac{69}{2}$

$4 x = \frac{55}{2}$

$x = \frac{55}{2 \times 4}$

color(blue)(x=55/8