Graphing Systems of Linear Inequalities

This video tutorial covers graphing systems of two linear inequalities. It begins with an introduction to the concept and the learning goal, followed by an explanation of what systems of inequalities are and how their solutions are represented. The tutorial then demonstrates how to graph these systems on a coordinate plane, using example problems to illustrate the process. It also discusses how to determine if specific points are part of the solution set. The video concludes with additional practice problems and a discussion on cases where no solution exists, particularly when dealing with parallel lines.

What is a system of inequalities?

• A set of equations with the same variables

• A set of equations with different variables

• A set of two or more inequalities with the same variables

• A single inequality with multiple variables

What represents the solution set in a graph of a system of inequalities?

• The union of the shaded regions

• The intersection of the shaded regions

• The entire coordinate plane

• The area outside the shaded regions

How do you graph an inequality that does not include the boundary line?

• Use a double line

• Use a thick line

• Use a dashed line

• Use a solid line

Which point is part of the solution set for the inequalities y < 2x + 2 and y ≥ -x - 3?

• (0, 0)

• (4, -3)

• (6, 0)

• (-2, 3)

Which point is NOT part of the solution set for the inequalities y ≤ 1/2x and y < -x - 4?

• (0, -4)

• (-3, -6)

• (0, 0)

• (0, -5)

What type of line is used to graph y ≤ 1/2x?

• Double line

• Dashed line

• Solid line

• Thick line

What is the solution set for the inequalities y < -1/2x + 2 and y ≥ -6?

• The area below both lines

• The area between the lines

• No solution

• The area above both lines

What happens when two inequalities in a system are parallel and shaded in opposite directions?

• There is no solution

• There is one solution

• There are infinite solutions

• The solution is the entire plane

If two parallel lines are shaded in the same direction, what can be said about the solution set?

• The solution is the area between the lines

• There are infinite solutions

• There is one solution

• There is no solution

Does the presence of parallel lines in a system of inequalities always mean there is no solution?

• Yes, if the lines are vertical

• No, it depends on the direction of shading

• Yes, always

• No, if the lines are horizontal