Exploring Systems of Linear Inequalities

This video tutorial covers solving systems of linear inequalities. It begins with an introduction to linear inequalities and graphing basics, including how to draw lines and shade regions. The tutorial then explains how to graph each inequality and find the overlapping region that represents the solution. Several example problems are worked through, demonstrating the process of solving inequalities and identifying solutions. The video concludes with a word problem that applies these concepts to a real-world scenario, illustrating how to write and graph inequalities to find possible solutions.

What is a system of linear inequalities?

• A set of parallel lines

• A quadratic equation

• Two or more linear inequalities graphed together

• A single linear equation

When graphing a linear inequality, what type of line is used for a 'greater than' symbol?

• Dotted line

• Dashed line

• Thick line

• Solid line

In the inequality y > -x - 1, where should the shading be done?

• Below the line

• Above the line

• On the line

• To the left of the line

What is the y-intercept of the inequality y < x - 5?

• 5

• 1

• 0

• -5

How do you transform the inequality x - 4y ≤ 24 into slope-intercept form?

• Add x to both sides

• Subtract x from both sides

• Divide both sides by 4

• Multiply both sides by 4

What happens to the inequality symbol when you divide both sides by a negative number?

• It becomes an equal sign

• It disappears

• It stays the same

• It flips

What is the slope of the line represented by the inequality y ≥ 1/4x - 6?

• -6

• 6

• -1/4

• 1/4

If two lines are parallel, what can be said about their slopes?

• They are perpendicular

• One is zero

• They are negative reciprocals

• They are equal

In the word problem, what does x represent?

• Number of dogs

• Number of birds

• Number of cats

• Total number of pets

What is the inequality representing the total number of cats and dogs in Sarah's pet store?

• x + y ≥ 16

• x - y ≥ 16

• x + y ≤ 16

• x - y ≤ 16