# How do you solve 3x+y=3 and x+2y=-4?

Aug 14, 2015

The solutions for the equation are
color(blue)(x=2,y=-3

#### Explanation:

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

x+2y=−4 , multiplying this equation by $3$
color(blue)(3x)+6y=−12 ....... equation $\left(2\right)$

Now we can solve through elimination as term $\textcolor{b l u e}{3 x}$ is common to both equations.

Subtracting equation $\left(2\right)$ from $\left(1\right)$
$\cancel{\textcolor{b l u e}{3 x}} + y = 3$
$- \cancel{\textcolor{b l u e}{3 x}} - 6 y = + 12$

$- 5 y = 15$
color(blue)(y=-3

Substituting the value of $y$ in equation $1$
x+2y=−4
x+2 * (-3)=−4
x-6=−4
color(blue)(x=2