Graphing Systems of Inequalities in Algebra 1

This video tutorial covers graphing systems of linear inequalities. It begins with an introduction to the concept, explaining the difference between graphing linear equations and inequalities. The tutorial then provides step-by-step instructions for graphing multiple examples, highlighting key concepts such as shading regions and determining solution areas. The video concludes with additional examples and emphasizes the importance of understanding symbols and shading techniques.

What is the key difference between solving an equation and solving an inequality?

• Equations and inequalities both have one solution.

• Equations have multiple solutions, while inequalities have one solution.

• Equations and inequalities both have multiple solutions.

• Equations have one solution, while inequalities have multiple solutions.

When graphing an inequality, what does shading represent?

• The area where the inequality is true.

• The exact solution to the inequality.

• The points that are not solutions to the inequality.

• The area where the inequality is not true.

In the first example, what type of line is used for the inequality y ≤ -2x + 4?

• Dotted line

• Solid line

• Dashed line

• No line

For the inequality y > 1/2x - 5, where should you shade?

• No shading required

• On the line

• Below the line

• Above the line

What is the solution area for a system of inequalities?

• The entire graph.

• The area where neither inequality is true.

• The area where both inequalities are true.

• The area where only one inequality is true.

In the second example, what type of line is used for the inequality y > -2x + 4?

• Dashed line

• No line

• Solid line

• Dotted line

How can you test if a point is a solution to a system of inequalities?

• By substituting the point into both inequalities and checking if both are true.

• By checking if the point lies on the line.

• By checking if the point lies outside the shaded region.

• By substituting the point into one of the inequalities.

For the inequality y < 1/2x - 5, where should you shade?

• Above the line

• No shading required

• On the line

• Below the line

What type of line is used for the inequality x > -2?

• Solid vertical line

• Solid horizontal line

• Dashed vertical line

• Dashed horizontal line

In the final example, what is the solution region for the system of inequalities?

• The entire graph.

• The area where neither inequality is true.

• The area where both inequalities are true.

• The area where only one inequality is true.