# Solve the following system 3y + x = -3 and -6y + x = -12 using the graphing method?

Mar 28, 2015

Since both of the given equations a linear we only need 2 points for each equation to draw their lines and it is most convenient to use the axis intercept points

$3 y + x = - 3$ will give us $\left(x , y\right)$ intercepts at
$\left(0 , - 1\right)$ and $\left(- 3 , 0\right)$

$- 6 y + x = - 12$ will give us $\left(x , y\right)$ intercepts at
$\left(0 , 2\right)$ and $\left(- 12 , 0\right)$

On graph paper draw a straight line through both
$\left(0 , - 1\right)$ and $\left(- 3 , 0\right)$ for $3 y + x = - 3$
and another straight line through both
$\left(0 , 2\right)$ and $\left(- 12 , 0\right)$ for $- 6 y + x = - 12$

We can then read the point of intersection of the two lines from the graph as $\left(x , y\right) = \left(- 6 , 1\right)$