# How do you graph the inequality #3-x>0# and #y+x< -6#?

##### 1 Answer

See below.

#### Explanation:

First we write the inequalities as linear equations, and the graph these. Remember to use a dashed line, as these are not equal to inequalities, so the line itself will not be an included region.

We now graph these:

With graph plotted, we can see that there are four possible regions.

**A** , **B** , **C** and **D**

The required region has to satisfy both inequalities, so we test a set of coordinates in each region. We can save some work by realising that if a coordinate in a region fails for the first inequality we test, then the region can't be the required region and it is not necessary to test the other inequality as well.

**Region A**

Coordinates:

**TRUE**

**FALSE**

Region **A** is not the required region.

**Region B**

Coordinates:

**TRUE**

**FALSE**

Region **B** is not the required region.

**Region C**

Coordinates:

**TRUE**

**TRUE**

Region **C** is a required region.

We do not need to test region **D**. As can be seen from the graph above if **C** is an included region and is to the left of the line

Shade the required region **C**