# How do you solve the following system?: 8x +y =3 , 4x +12y = -4

Nov 11, 2015

The solution for the system of equations is:
color(blue)(x=10/23, y=-11/23

#### Explanation:

$\textcolor{b l u e}{8 x} + y = 3$....equation $1$

4x+12y=−4, multiplying this equation by $2$
color(blue)(8x)+24y=−8......equation $2$

Now, we solve by elimination :
Subtracting equation $2$ from $1$

$\cancel{\textcolor{b l u e}{8 x}} + y = 3$
$- \cancel{\textcolor{b l u e}{8 x}} - 24 y = + 8$

$- 23 y = 11$

$y = \frac{11}{-} 23$

y=color(blue)(-11/23

Now we substitute $y$ in any of the equations to find $x$

$8 x + y = 3$

$8 x - \frac{11}{23} = 3$

$8 x = 3 + \frac{11}{23}$

$8 x = \frac{80}{23}$

$x = \frac{\cancel{80}}{23 \cdot \cancel{8}}$

color(blue)(x =10/23