# How do you graph the system of inequalities y<2x + 2, y> -x - 1?

Dec 8, 2017

See below.

#### Explanation:

First graph the equations $y = 2 x + 2$ and $y = - x - 1$. Use a dashed line as these are $<$ and $>$ and not $\le$ and $\ge$ inequalities. This will give you the boundary lines.

Test an $\left(x , y\right)$ coordinate in each section, to see which region is included or excluded.

Looking at graph, test coordinates in Areas A, B , C and D. These coordinates must satisfy both inequalities.

A $\left(- 1 , 3\right)$

$- 1 < 2 \left(- 1\right) + 3 \textcolor{w h i t e}{888}$ TRUE

$- 1 > - \left(- 1\right) - 1 \textcolor{w h i t e}{888}$ FALSE

A is an excluded region.

B$\left(1 , 1\right)$

$1 < 2 \left(1\right) + 2 \textcolor{w h i t e}{888}$ TRUE

$1 \succ \left(1\right) - 1 \textcolor{w h i t e}{888}$ TRUE

B is the included region.

Since we have found included region, we do not need to test any further.