Graphing Systems of Linear Inequalities

The video tutorial covers graphing systems of linear inequalities, checking solutions, and identifying solution sets. It explains how to graph each inequality, find the intersection of solution areas, and verify solutions using ordered pairs. The tutorial includes practice problems to reinforce learning and emphasizes the importance of identifying solution areas through graphing and shading techniques.

What is a system of linear inequalities?

• A set of inequalities with different variables

• A set of two or more linear inequalities in the same variables

• A set of equations with no variables

• A single linear equation

What defines the solution set of a system of linear inequalities?

• The area below the graph

• The area above the graph

• The intersection of the solutions of the inequalities

• The union of all solutions

How do you determine if an ordered pair is a solution to a system of inequalities?

• It must satisfy only one inequality

• It must be a point on the graph

• It must be outside the shaded region

• It must satisfy all inequalities in the system

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

• Find the intersection of the graphs

• Graph each inequality on the same coordinate plane

• Draw a single line

• Shade the entire graph

What does the shaded region in a graph of inequalities represent?

• The solution to the system of inequalities

• The solution to one inequality

• The area outside the solution

• The area above the graph

What should you do if there is no overlap in the shaded regions of a graph?

• Change the inequalities

• Draw a new line

• Conclude that there is no solution

• Shade the entire graph

How can you verify the accuracy of a system of inequalities from a graph?

• By checking if the lines are parallel

• By testing points within the shaded region

• By ensuring the graph is colorful

• By counting the number of lines