If you need extra practice, follow the instructions below for Example 1, Example 2, Example 3.

Use the applet to graph each system of inequalities shown below.

Once you have graphed each system, determine if the origin (0 , 0) is part of the solution region.

Example 1:

y ≤ 3x − 1
y ≥ -2x +5

Example 2:

y ≤ 3x + 3
y ≥ -one-half 1 2 x +5

Example 3:

y ≥ 5x + 4
y ≤ 5x − 1

Answer the following questions in your notes:

• How do you know if the origin is or is not a solution to each system of inequalities?
• How is Example 3 different from Examples 1 and 2?

Did you write something like this?

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Check Your Answers

1. (0 , 0) is a solution for Example 2 only.
2. Example 3 is different from Examples 1 and 2 because there is no solution region.