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

Mar 15, 2016

Solution: $x = 3$ and $y = 5$

#### Explanation:

Step one. Solve both equations for $y$. The first equation you provided is already equal to $y$, so just copy it.

Then solve the second equation for $y$:

$2 x - y = 1$
$\textcolor{w h i t e}{. .} + y \textcolor{w h i t e}{.} + y$ $\textcolor{w h i t e}{. . x}$add y to both sides
$2 x = 1 + y$
$- 1 \textcolor{w h i t e}{.} - 1$ color(white)(xxxx;)subtract 1 from both sides
$2 x - 1 = y$

Now, either plotting points or plugging into your graphing utility, you can first graph the first equation:

$g r a p h \left\{3 x - 4 \left[- 1 , 3 , - 6 , 10\right]\right\}$

Then, on the same graph paper, either plot points or plugging into your graphing utility, you draw the second graph on top of this one.

$g r a p h \left\{\left(y - 2 x + 1\right) \left(y - 3 x + 4\right) = 0 \left[- 0.4 , 4.5 , - 2 , 8\right]\right\}$

Observing closely where they cross, gives the solution

$x = 3$ and $y = 5$.