Understanding Systems of Inequalities

Luis has a $25 gift card for an online retailer selling digital music and games. Each song costs $0.89, and each game costs $1.99. He wants to buy at least 15 items. The video sets up a system of inequalities to represent this scenario and uses a graph to identify possible purchase combinations. The constraints are that the total cost must not exceed $25, and the total number of items must be at least 15. The video demonstrates how to graph these inequalities and find the region of overlap, which represents the valid combinations of songs and games Luis can purchase.

What is the total value of the gift card Luis received?

• $25

• $30

• $20

• $15

How much does each song cost?

• $1.99

• $1.29

• $2.49

• $0.89

What is the cost of each game?

• $0.89

• $1.49

• $1.99

• $2.99

What is the first constraint in the problem?

• The total cost must be exactly $25.

• The total cost must be more than $25.

• The total cost must be less than $20.

• The total cost must be less than or equal to $25.

What is the second constraint in the problem?

• Luis must buy at least 15 items.

• Luis must buy more than 20 items.

• Luis must buy less than 15 items.

• Luis must buy exactly 15 items.

What form is used to express the inequalities for graphing?

• Standard form

• Slope-intercept form

• Point-slope form

• Quadratic form

What is the slope of the line representing the first constraint?

• -1

• -0.89

• -0.447

• -0.5

What is the y-intercept of the line representing the first constraint?

• 25

• 10

• 15

• 12.56

Which region on the graph represents the feasible solutions?

• Outside the lines

• Between the lines

• Below both lines

• Above both lines

Why are only integer coordinates considered in the feasible region?

• Because the graph only shows integer values

• Because Luis can only buy whole items

• Because Luis can buy fractional items

• Because fractional values are not allowed in inequalities