Solving Systems of Inequalities Graphically

The video tutorial demonstrates how to solve real-life systems of inequalities graphically. It uses a concert ticket sales problem to illustrate the process of setting up inequalities based on ticket numbers and costs. The tutorial guides viewers through graphing these inequalities using a calculator, tracing and plotting points, and identifying the solution area where the inequalities overlap. The goal is to find a combination of ticket sales that satisfies both the number and cost constraints.

What is the maximum number of tickets that can be sold at the concert?

• 120 tickets

• 200 tickets

• 160 tickets

• 100 tickets

How much does each adult ticket cost?

• $4

• $3

• $2

• $1

What is the minimum amount of money the school wants to make from the concert?

• $180

• $120

• $140

• $160

Which inequality represents the constraint on the number of tickets?

• 2x + y <= 160

• 2x + y >= 160

• x + y <= 120

• x + y >= 120

What does the inequality '2x + y >= 160' represent in this context?

• Minimum revenue required

• Minimum number of tickets

• Maximum number of tickets

• Maximum revenue possible

How is the inequality 'x + y <= 120' graphed on a calculator?

• With shading above

• As a dotted line

• With shading below

• As a solid line

Where should the graph be shaded for the inequality '2x + y >= 160'?

• Above the line

• Below the line

• On the line

• No shading needed

What feature of the graphing calculator is used to find points on the graph?

• Zoom

• Window

• Trace

• Plot

What does the area of overlap in the graph represent?

• Invalid ticket combinations

• Possible ticket combinations

• Minimum ticket area

• Maximum revenue area

Which ticket combination meets both requirements?

• 80 adult, 40 student

• 90 adult, 20 student

• 100 adult, 20 student

• 70 adult, 50 student