# How do you solve by graphing y = 4x + 4 and 3x + 2y = 12?

May 29, 2015

A graph of the given equations (see below) may give an indication of the general area of the solution; but (unless it is drawn at a very large scale) it is unlikely to provide an exact solution.

Both equations are linear and the easiest point to evaluate are the x and y intercepts

$y = 4 x + 4$
$\textcolor{w h i t e}{\text{XXXX}}$ has a y-intercept at $\left(0 , 4\right)$ and an x-intercept at $\left(- 1 , 0\right)$

$3 x + 2 y = 12$
$\textcolor{w h i t e}{\text{XXXX}}$ has a y-intercept at $\left(0 , 6\right)$ and an x-intercept at $\left(4 , 0\right)$

Using analytic methods (non-graphing) give the solution
$\left(x , y\right) = \left(\frac{4}{11} , \frac{60}{11}\right)$