Understanding Systems of Linear Inequalities

The video tutorial explains how to solve a system of linear inequalities by graphing. It covers the process of graphing each inequality, identifying the boundary lines, and shading the appropriate regions. The tutorial emphasizes finding the double-shaded region, which represents the solution set that satisfies both inequalities. The video also demonstrates using test points to verify the correct shading of regions.

What is the first step in solving a system of linear inequalities?

• Solve the inequalities algebraically.

• Use a calculator to find the solution.

• Find the intersection of the inequalities.

• Graph the solution of each inequality separately.

When graphing the first inequality, what does a dashed boundary line indicate?

• The inequality is equal to.

• The inequality is less than.

• The inequality is less than or equal to.

• The inequality is greater than.

How can you determine which side of the boundary line to shade for the first inequality?

• By checking the slope of the line.

• By drawing a solid line.

• By using a test point.

• By calculating the y-intercept.

What is the slope of the second inequality's boundary line?

• +3/2

• -6

• -2/3

• +2/3

For the second inequality, what does a solid boundary line represent?

• The inequality is less than.

• The inequality is greater than.

• The inequality is greater than or equal to.

• The inequality is less than or equal to.

What is the y-intercept of the second inequality?

• -2

• +2

• -6

• 0

What is the solution to a system of linear inequalities?

• The region that is shaded twice.

• The intersection of the boundary lines.

• The area above the first line.

• The area below the second line.

In the context of this video, what does the double-shaded region represent?

• The area that satisfies only one inequality.

• The area that is outside the graph.

• The area that does not satisfy any inequality.

• The area that satisfies both inequalities.

What is the purpose of using arrows instead of shading in the video?

• To avoid using too much ink.

• To highlight the double-shaded region.

• To indicate the direction of the slope.

• To make the graph look cleaner.

What will be covered in the next video?

• A summary of the previous lessons.

• An introduction to quadratic inequalities.

• A review of the current example.

• A new example of solving linear inequalities.