Graphing Systems of Inequalities

The video tutorial covers graphing systems of linear inequalities, focusing on identifying shading regions where solutions exist. It explains the process of graphing inequalities using x-intercepts and y-intercepts, determining whether lines are solid or dotted, and testing points to decide shading areas. The tutorial also addresses graphing in slope-intercept form and discusses scenarios with no solution due to parallel lines. The goal is to find regions where shading overlaps, indicating solutions to the system of inequalities.

What is the primary difference between graphing systems of linear equations and systems of linear inequalities?

• Linear inequalities involve shading regions.

• Linear equations have no shading.

• Linear inequalities always have intersection points.

• Linear equations involve shading regions.

When graphing the inequality x + y > 1, what type of line should be used?

• Solid line

• Dotted line

• Dashed line

• No line

How do you determine which side of the line to shade for the inequality x + y > 1?

• Do not shade any side.

• Shade both sides of the line.

• Shade the side where the test point makes the inequality false.

• Shade the side where the test point makes the inequality true.

For the inequality x - 3y > 3, what is the x-intercept?

• (0, 3)

• (3, 0)

• (0, -1)

• (3, -1)

What is the solution region for a system of linear inequalities?

• The region where the shading does not overlap.

• The entire graph.

• The region where the lines intersect.

• The region where the shading overlaps.

When graphing y ≥ x - 1, what type of line should be used?

• No line

• Solid line

• Dashed line

• Dotted line

For the inequality y ≤ -1/2x + 2, what is the slope?

• 2

• -1/2

• 1/2

• -2

How do you determine the solution region for a system of inequalities in slope-intercept form?

• By solving the equations algebraically.

• By finding the intersection points.

• By using only one of the inequalities.

• By shading the regions and finding the overlap.

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

• There is one solution.

• There is no solution.

• There are infinite solutions.

• The solution is the entire graph.

For the inequality 3x + y < 3, what is the y-intercept?

• (0, 1)

• (0, -3)

• (3, 0)

• (0, 3)