Solving Systems of Linear Inequalities

Mr. Buffington explains how to graph systems of linear inequalities. The video covers the basics of graphing linear equations and inequalities, and then demonstrates how to graph two inequalities: y > 3x + 2 and y ≤ -2x - 3. The solution to the system is found by identifying the overlapping shaded region on the graph, which represents the set of points that satisfy both inequalities. The video also provides a method to verify solutions by testing points within the shaded area.

What is the prerequisite knowledge needed before starting to graph systems of linear inequalities?

• Understanding quadratic equations

• Knowledge of trigonometric functions

• Knowing how to graph linear equations and inequalities

• Familiarity with polynomial functions

In a system of linear inequalities, what represents the solution region?

• The intersection of the lines

• The area above the first line

• The area below the second line

• The area where the shaded regions overlap

What is the y-intercept of the inequality y > 3x + 2?

• 0

• 1

• 2

• 3

How should the line be drawn for the inequality y > 3x + 2?

• Thick line

• Dashed line

• Solid line

• Double line

For the inequality y > 3x + 2, which region should be shaded?

• To the left of the line

• Below the line

• On the line

• Above the line

What is the y-intercept of the inequality y ≤ -2x - 3?

• 3

• -3

• -2

• 2

How should the line be drawn for the inequality y ≤ -2x - 3?

• Solid line

• Dashed line

• Thick line

• Double line

For the inequality y ≤ -2x - 3, which region should be shaded?

• Below the line

• To the right of the line

• Above the line

• On the line

What color represents the solution region for both inequalities in the combined graph?

• Blue

• Red

• Purple

• Green

How can you verify if a point is a solution to the system of linear inequalities?

• Check if it lies below the line

• Check if it lies on the line

• Plug the point into both inequalities and see if they hold true

• Check if it lies above the line