Exploring System of Inequalities

The video tutorial covers solving systems of inequalities by graphing. It begins with an introduction to inequalities, followed by graphing techniques and shading regions to find solutions. The tutorial then tests specific points to verify solutions. A word problem involving transportation logistics is introduced, where inequalities are used to model the situation. The video analyzes cost and budget constraints, and concludes by finding solutions that satisfy both conditions.

What are the unknowns in the first system of inequalities?

• X and Y

• A and B

• M and N

• X and Z

Why is the red line dashed in the graph?

• Because y can be equal to 4X + 2

• Because y cannot equal 4X + 2

• Because y is less than 4X + 2

• Because y is greater than 4X + 2

What does the shaded region between the lines represent?

• The area where y is less than both lines

• The area where y is greater than both lines

• The area where solutions satisfy both inequalities

• The area where solutions satisfy only one inequality

Which point is tested to verify if it satisfies both conditions?

• (0, 0)

• (-3, -5)

• (-2, -4)

• (1, 1)

What is the maximum number of people that can be transported by the student council?

• 180

• 155

• 200

• 100

How many students can a minivan hold?

• 8

• 4

• 6

• 10

What is the budget for renting vehicles?

• $500

• $600

• $700

• $800

How much does it cost to rent one SUV?

• $22

• $25

• $18

• $20

Can the student council rent 40 SUVs and stay within budget?

• Only if they increase the budget

• Only if they rent fewer minivans

• No, they cannot

• Yes, they can

What is the combination of vehicles that allows all students to go and stay under budget?

• 22 minivans and 6 SUVs

• 20 minivans and 10 SUVs

• 24 minivans and 5 SUVs

• 18 minivans and 8 SUVs