Problem Solving Systems of Linear Equations

Which of the following points is a solution to the system of equations below?
x + 2y ≥ 4
3x − 2y < 4
Take your time!

• (0, 0)

• (2, 1)

• (2, 2)

• (-1, 1)

Jenna sold 10 packages of sugar cookies and 2 packages of oatmeal cookies for $56. Maggie sold 9 packages of sugar cookies and 3 packages of oatmeal cookies for $60. What is the price of 1 pack of sugar cookies and 1 pack of oatmeal cookies?

• Sugar Cookies $5

  Oatmeal Cookies $3

• Sugar Cookies $4

  Oatmeal Cookies $8

• Sugar Cookies $2

  Oatmeal Cookies $6

• Sugar Cookies $3

  Oatmeal Cookies $6

JoAnn likes her job as a baby-sitter, but it pays only $3 per hour. She has been offered a job as a tutor that pays $6 per hour. Because of school, her parents only allow her to work a maximum of 15 hours per week. How many hours can JoAnn tutor and baby-sit and still make at least $66 per week? How much does she make?

• b + t < 15

  3b + 6t > 66

• b + t > 15

  3b + 6t < 66

• 3b + 6t > 15

  b + t < 66

• 3b + 6t < 15

  b + t < 66

8x + 14y = 4

-6x - 7y = -10

• (4, -2)

• (-2, 4)

• (0, 3)

• (-4, -2)

Ride and Transport are two new ride sharing companies in Colorado. Ride is charging $2 for pick up fees and then $2.50 per mile. Transport is charging only $2.70 per mile. How many miles will it take for both companies to charge the same amount? Write a system of equations to solve.

• 27 miles

• 10 miles

• 270 miles

• 100 miles

Your friend rents 10 chairs and 2 tables for $300. Another friend rents 8 chairs and 4 tables for $360. How much does a chair and a table cost? Write a system of equations to solve.

• Chairs $2 Tables $5

• Chairs $50 Tables $20

• Chairs $10 Tables $15

• Chairs $20 Tables $50

You and your brother each decide to open a savings account. You open your account at Elsa’s Banking Branch. Your brother opens his account at Anna’s Banking Company. You put $50 in the bank and your account earns $4 per week in interest. Your brother puts $150 in his account but only earns $2 per week in interest. How many weeks will it take for both your brother and your account to have the same balance? Write a system of linear equations to solve the problem.

• 200 weeks

• 300 weeks

• 50 weeks

• 250 weeks

The basketball team is planning a fundraiser to sell shirts to raise money for new kicks. They plan to sell the shirts for $15 each. The company they order the shirts from charges the team a set up fee of $150 and $7.50 for each shirt printed. How many shirts must they sell to break even? Write a system of linear equations to solve the problem.

• 20 shirts

• 300 shirts

• 150 shirts

• 30 shirts

Macy starts with $20 in her bank account and she saves $5 each week. Robby has $100 in his bank account, and he saves $2.50 each week. After how many weeks will Macy and Robby have the same amount in their accounts and how much money will that be? Write a system of equations to solve.

• 25 weeks; $160

• 32 weeks; $180

• 20 weeks; $120

• 22 weeks; $135

Alex and Billy are running laps. According to the graph, how long will it take for the two boys to run the same distance?

• 20 minutes

• 15 minutes

• 10 minutes

• 5 minutes