Verifying Graphs of Systems of Inequalities

This video tutorial teaches how to verify the accuracy of graphed systems of inequalities by using points from different regions of the graph. It explains how to determine if the correct half-plane is shaded and addresses common misconceptions, such as the belief that only the intersection of lines needs checking. The tutorial provides a step-by-step guide to graphing a system of inequalities, shading regions, and verifying solutions by checking points in various regions. It concludes with methods to ensure graph accuracy, emphasizing the importance of verifying points that satisfy both or only one inequality.

What is a simple method to verify if the correct half-plane was shaded for an inequality?

• Check if the intersection of lines is shaded.

• Ensure the entire graph is shaded.

• Use a point from the shaded region and substitute it into the inequality.

• Use a point from the non-shaded region.

Why might someone mistakenly think the intersection of lines is the only solution for a system of inequalities?

• Because it is always in the shaded region.

• Because it is the easiest point to calculate.

• Because it is the only point that satisfies all inequalities.

• Because it is a common method used for solving systems of equations.

In the example provided, what color is used to shade the intersection of the half-planes?

• Yellow

• Red

• Green

• Blue

Which point was used to verify that it satisfies both inequalities in the example?

• (0, 0)

• (1, 2)

• (3, 4)

• (6, 7)

What happens if a point is only in the green region of the graph?

• It satisfies neither inequality.

• It satisfies both inequalities.

• It satisfies only the inequality represented by the green region.

• It is not a valid point for the graph.

What is the significance of a point in the non-shaded region?

• It satisfies only one inequality.

• It is the intersection point.

• It satisfies both inequalities.

• It satisfies neither inequality.

What is one method to check the accuracy of a graphed system of inequalities?

• Locate points that satisfy both inequalities and verify they are in the intersection.

• Use only the intersection point.

• Check points only in the non-shaded region.

• Shade the entire graph.