Exploring the System of Linear Inequalities

The video tutorial covers the topic of graphing systems of linear inequalities. It begins with an introduction to linear inequalities and explains how to graph them using the y-intercept and slope. The tutorial demonstrates graphing two inequalities, one with a solid line and the other with a dotted line, and explains how to determine the solution region by shading. It also covers how to check if specific points are solutions to the system. The video concludes with a review and instructions for practice.

What is a system of linear inequalities?

• A single linear equation

• Two or more linear equations or inequalities

• A quadratic equation

• A polynomial equation

When graphing inequalities, where do you start?

• With the y-intercept

• With the slope

• With the origin

• With the x-intercept

How do you determine the slope from the equation y = 2x - 1?

• The slope is 0

• The slope is 1

• The slope is -1

• The slope is 2

What type of line is used for the inequality y ≤ 2x - 1?

• No line

• Dotted line

• Dashed line

• Solid line

For the inequality y > x/3 + 1, which region should be shaded?

• No shading required

• Below the line

• Above the line

• On the line

What does a dotted line represent in graphing inequalities?

• The inequality is cubic

• The inequality is quadratic

• The inequality does not include the line

• The inequality includes the line

If a point lies on a dotted line, is it a solution to the inequality?

• Only if it is a solid line

• Yes, always

• Only if it is shaded

• No, never

Which point is a solution if it lies in both shaded regions?

• (2, 3)

• (2, 1)

• (3, 2)

• (-5, 2)

What is the y-intercept of the equation y = -1/2x + 5?

• 5

• -1/2

• 1

• 0

In the final graph, which region represents the solution to the system?

• The region shaded in green

• The region shaded in pink

• The region shaded in orange

• The region shaded in blue