How do you solve the system of equations: 3x+y=3 and x+2y=-4?

Aug 15, 2015

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

Explanation:

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

$x + 2 y = - 4$, multiplying this equation by $3$
$\textcolor{b l u e}{3 x} + 6 y = - 12$........equation $2$

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

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

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

Finding $x$ by substituting $y$ in equation $2$
$x + 2 y = - 4$
$x = - 4 - 2 y$
$x = - 4 - 2 \cdot - 3$
$x = - 4 + 6$
color(blue)(x=2