Exploring Systems of Inequalities

The video tutorial covers graphing systems of linear inequalities, focusing on determining whether lines should be dashed or solid and how to shade regions based on inequality signs. It provides two examples, demonstrating how to graph inequalities, identify slopes and intercepts, and find solution sets in double shaded areas. The tutorial concludes with checking specific points to determine if they lie within the solution set.

What type of line is used when the inequality does not include 'equal to'?

• Dotted line

• Curved line

• Dashed line

• Solid line

When graphing the inequality y < 3x + 2, where should the shading be?

• To the left of the line

• Below the line

• Above the line

• On the line

In Example 1, what is the slope (m) of the line 3x + y < 2?

• -1

• 3

• -3

• 1

For the inequality y + 1 ≥ x, what type of line should be drawn?

• Dashed line

• Dotted line

• Solid line

• Curved line

Which point is in the solution set for the system in Example 1?

• (-3, 3)

• (0, -4)

• (1, 4)

• (0, 0)

What is the y-intercept (b) of the line 8x + 4y ≤ 12?

• 2

• 1

• -2

• 3

For the inequality y < 1/2x - 2, where should the shading be?

• On the line

• Above the line

• Below the line

• To the left of the line

In Example 2, what type of line is used for the inequality y + 2 < 1/2x?

• Dotted line

• Curved line

• Dashed line

• Solid line

Which point is in the solution set for the system in Example 2?

• (0, 0)

• (-2, -3)

• (5, -1)

• (0, -3)

Why is the point (-2, -3) not a solution in Example 2?

• It is on a solid line

• It is on a dashed line

• It is outside the shaded region

• It is in the double shaded area