Understanding Systems of Linear Inequalities

The video tutorial explains how to solve systems of linear inequalities using the graphing method. It covers the concept of solution sets, special cases with no solutions, and provides examples for practice. Students are encouraged to pause the video to graph inequalities and check their work against provided solutions. The tutorial concludes with a recommendation for further practice using additional examples available online.

What is a system of linear inequalities?

• A set of inequalities with two or more variables

• A set of equations with no variables

• A single inequality with two variables

• A set of equations with one variable

Which method is used to solve systems of linear inequalities in this tutorial?

• Substitution method

• Elimination method

• Graphing method

• Matrix method

What does the solution set of a system of inequalities represent?

• A single point that satisfies all inequalities

• A set of points that satisfy at least one inequality

• A line that satisfies all inequalities

• A set of points that satisfy all inequalities

What is indicated by the purple area in the graph of a system of inequalities?

• The area that satisfies the first inequality only

• The area that satisfies only one inequality

• The area that satisfies both inequalities

• The area that does not satisfy any inequality

What happens when the lines in a system of inequalities are parallel and do not overlap?

• There is no solution

• There are infinite solutions

• There is a unique solution

• The solution is the entire plane

In Example 1, what type of line is used to graph the inequality y > x?

• Dashed line

• Solid line

• Dotted line

• Thick line

In Example 1, what does the shading above the line y > x represent?

• The area that satisfies y = x

• The area that satisfies y > x

• The area that satisfies y ≤ x

• The area that satisfies y < x

In Example 1, what is the significance of the area shaded by both inequalities?

• It is the area that satisfies the first inequality only

• It is the area that does not satisfy any inequality

• It is the area that satisfies only one inequality

• It is the solution set

In Example 3, what type of line is used to graph the inequality y ≤ 2x + 3?

• Thick line

• Dotted line

• Dashed line

• Solid line

In Example 3, what does the shading below the line y ≤ 2x + 3 represent?

• The area that satisfies y ≥ 2x + 3

• The area that satisfies y ≤ 2x + 3

• The area that satisfies y = 2x + 3

• The area that satisfies y > 2x + 3