Exploring System of Linear Inequalities

This video tutorial covers the process of graphing solutions to systems of linear inequalities. It begins with an introduction to the concept and outlines the steps involved in graphing such systems. The video provides multiple examples, starting with simple systems and progressing to more complex ones, demonstrating how to graph and shade the solution regions. It also discusses the importance of identifying double-shaded regions and offers tips for using test points to determine shading areas. The tutorial concludes with advanced graphing techniques for systems with solid lines.

What is the main goal of the video?

• To understand polynomial functions

• To learn about linear equations

• To graph the solution to a system of linear inequalities

• To solve quadratic equations

What is the first step in graphing the solution to a system of linear inequalities?

• Solve the inequalities algebraically

• Graph and shade the solution to the first linear inequality

• Find the intersection points

• Graph and shade the solution to the second linear inequality

What does the double-shaded region represent in a system of linear inequalities?

• The area outside the solution

• The solution to the system of inequalities

• The solution to the second inequality

• The solution to the first inequality

When graphing the inequality X > -4, which side of the line X = -4 should be shaded?

• Left side

• Below the line

• Right side

• Above the line

For the inequality Y ≤ 2, what type of line is used and which region is shaded?

• Dashed line, below the line

• Solid line, above the line

• Solid line, below the line

• Dashed line, above the line

In the second example, what is the slope of the line Y = 3X - 4?

• 4

• 3

• 2

• 1

For the inequality Y < -X + 2, which region is shaded?

• Below the line

• Left of the line

• Right of the line

• Above the line

In the third example, what are the intercepts of the line X - 2Y = 4?

• (0, 2) and (-4, 0)

• (0, -2) and (4, 0)

• (0, 4) and (2, 0)

• (0, -4) and (2, 0)

When testing the point (0,0) for the inequality X - 2Y ≤ 4, what is the result?

• True, shade the same side as the test point

• False, shade the opposite side

• True, shade the opposite side

• False, shade the same side

What is the final solution region for the system of inequalities in the third example?

• The region above both lines

• The region outside the two lines

• The region below both lines

• The region between the two lines