Exploring Systems of Linear Inequalities in Word Problems

The video tutorial covers systems of linear inequalities through word problems. It begins with an introduction to the topic, highlighting its difficulty for Algebra 1 students. The first problem involves Catherine, who needs to manage her work hours between babysitting and hostessing to meet her financial goals. The tutorial explains how to set up and solve the system of inequalities, including graphing the solution. The second problem features Clay, who sells chips and sodas at a concession stand. The tutorial guides viewers through setting up and solving the inequalities to determine possible sales combinations. The video emphasizes graphing techniques and using tools like Desmos for visualization.

What type of problems does the video focus on?

• Quadratic equations

• Systems of linear inequalities

• Trigonometric identities

• Calculus problems

How much does Catherine earn per hour from babysitting?

• $15

• $12

• $8

• $10

What is the maximum number of hours Catherine can work in a week?

• 20 hours

• 25 hours

• 30 hours

• 40 hours

Which method is suggested for converting linear inequalities for graphing?

• Factoring

• Completing the square

• Slope-intercept form

• Using the quadratic formula

What is the y-intercept of the inequality representing Catherine's earnings from both jobs?

• 15

• 22

• 20

• 18

Why does the teacher use two different colors while graphing the system of inequalities?

• To show the non-viable region

• To indicate errors

• To highlight the intercepts

• To differentiate between the lines

What is the minimum number of items Clay wants to sell at his concession stand?

• 40 items

• 30 items

• 35 items

• 25 items

How much profit does Clay make on each soda sold?

• $1.00

• $0.50

• $1.50

• $2.00

What is the slope of the inequality representing the number of sodas and chips Clay needs to sell?

• -4

• -3

• -2

• -1

Which combination of sodas and chips meets Clay's sales goals?

• 25 sodas and 30 chips

• 30 sodas and 25 chips

• 20 sodas and 35 chips

• 35 sodas and 20 chips