Graphing Systems of Inequalities

This video tutorial covers the concept of inequalities, explaining how they compare values and their applications in determining budgets. It includes two detailed examples of graphing systems of inequalities, demonstrating the steps to determine line types, plot points, and shade overlapping regions. The tutorial concludes with practice problems for viewers to test their understanding.

What does an inequality compare?

• Two values to determine if they are both negative

• Two values to determine if they are both positive

• Two values to determine if they are equal

• Two values to determine if one is less than, greater than, or not equal to the other

What is the first step in graphing the system of inequalities?

• Find the intercepts

• Determine if the line is dotted or solid

• Plot and graph

• Shade the overlapping parts

In the inequality X + Y < 2, what type of line is used?

• Double line

• Thick line

• Dashed line

• Solid line

For the inequality 2X - Y ≤ 4, what type of line is used?

• Double line

• Solid line

• Dashed line

• Thick line

In Example 2, what is the first inequality to be graphed?

• 2X - Y < 4

• X + Y < 5

• Y > 1

• X > 1

What is the result when substituting the point (1, 1) into the inequality X + Y < 5?

• True

• False

• Not applicable

• Undefined

When graphing X > 1, which side of the line is shaded?

• Left

• Top

• Right

• Bottom

What is the result when substituting the point (2, -3) into the inequality X > 1?

• Not applicable

• Undefined

• False

• True

When graphing Y > 1, which side of the line is shaded?

• Top

• Left

• Right

• Bottom

What is the result when substituting the point (-2, 2) into the inequality Y > 1?

• Undefined

• False

• True

• Not applicable