# How do you solve the system y=2x-4 and y= -3x+1 by graphing?

Jan 21, 2016

$\left(x , y\right) = \left(1 , - 2\right)$
(see below for graphing)

#### Explanation:

Determine 2 points for each given equation:
$\textcolor{red}{y = 2 x - 4}$
$\textcolor{w h i t e}{\text{XXX}}$using the intercepts:
$\textcolor{w h i t e}{\text{XXXXXX}} \left(\textcolor{red}{0 , - 4}\right) \mathmr{and} \left(\textcolor{red}{2 , 0}\right)$
$\textcolor{b l u e}{y = - 3 x + 1}$
$\textcolor{w h i t e}{\text{XXX}}$use the y-intercept
$\textcolor{w h i t e}{\text{XXXXXX}} \left(\textcolor{b l u e}{0 , 1}\right)$
$\textcolor{w h i t e}{\text{XXX}}$but the x-intercept is ugly (a fraction),
$\textcolor{w h i t e}{\text{XXX}}$so let's use $x = 2$ since we already need this $x$ value from the first equation.
$\textcolor{w h i t e}{\text{XXXXXX}} \left(\textcolor{b l u e}{2 , - 5}\right)$

Plot and join the points for $\textcolor{red}{y = 2 x - 4}$ and (separately) the points for $\textcolor{b l u e}{y = - 3 x + 1}$

Read the point of intersection directly from the graph as
$\textcolor{w h i t e}{\text{XXX}} \left(\textcolor{g r e e n}{1 , - 2}\right)$