# Graphing Systems of Inequalities

Practice Problems

How did you like the Systems of Inequalities examples? Did the color coding help you to identify the area of the graph that contained solutions? I hope so!

In order to complete these practice problems, you will need graph paper,
colored pencils or crayons, and a ruler. If you don't have colored
pencils or crayons, that's ok. You can draw horizontal lines for one
graph and vertical lines for another graph to help identify the area
that contains solutions.

Let's quickly review our steps for graphing a system of inequalities.

## Systems of Inequalities

- Graph the first inequality. (Pay attention to your boundary line
and make sure you shade the half plane that contains the solutions to
the inequality.)

- Graph the second inequality on the same graph. (Shade the correct
half plane in a different color or use a different design with your
pencil.)

- Identify the area that is shaded by BOTH inequalities. This is the solution to the system of inequalities.

Are you ready to practice a few on your own? Let's do it!

## Practice Problems

1. 2y < 4x - 6 and y __<__ 1/2x + 1

2. y > 2/3x - 7 and x < -3

3. 3x - 2y __<__ 2 and y __>__ -1

Now it's time to check your answers. Pay special attention to the boundary lines and the shaded areas.

## Solutions

This first problem was a little tricky because you had to first
rewrite the first inequality in slope intercept form. Dividing all
terms by 2, was your first step in order to be able to graph the first
inequality.

Now let's take a look at your graph for problem 2. This problem was a
little tricky because inequality number 2 was a vertical line.

### Problem 2

Problem 3 is also a little tricky because the first inequality is
written in standard form. The easiest way to graph this inequality is
to rewrite it in slope intercept form.

SPECIAL NOTE: Remember to reverse the inequality symbol when you multply or divide by a negative number!

### Problem 3

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Systems of Inequalities
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Practice Problems

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