Unit 3 Summary

Class: Algebra 1

Unit 3: Systems of Equations – Chapter 7

  1. Big Ideas:
  • Students will understand that systems of linear equations can be represented and solved using a variety of strategies.
  • Students will understand how to apply their knowledge of systems of equations to interpret and make judgments in real world situations.
  • Students will be able to recognize situations where a system of equations would be used to solve the problem.
  1. Topics that will be covered:
  1. Solving systems of equations by graphing
  2. Solving systems of equations by substitution
  3. Solving systems of equations by elimination
  4. Consistent, independent, dependent, and inconsistent systems
  5. Using systems of equations to solve real-life problems
  6. Determine the best method for solving systems of equations
  1. Essential Questions:
  • What is the best way to solve a particular system of equations?
  • What is the significance of the solution to a system of linear equations?
  • How do I know how many solutions a system of equations will have?
  • What are the benefits of having different types of strategies to solve systems of equations related to real-world situations?
  1. Sample questions to answer by the end of the unit:

1. A bank teller is counting $20 bills and $10 bills. There are 16 bills that total $200. Write and solve a system of equations to find the number of $20 bills and $10 bills.

2. Bob bought 8 hockey tickets for $59. Adult tickets cost $10 each and child tickets cost $3 each. How many adult tickets did he buy?

3. The length of a rectangle is 2 centimeters longer than its width. The perimeter is 16 centimeters. What are the length and width of the rectangle?

4. Which is the solution to the system of equations: 2x + y = 4

3x – y = -14

A. (-2, 8)

B. (-2, 0)

C. (2, 0)

D. (0, -2)

5. The concession stand sells pizza and drinks during football games. Jack bought 4 drinks and 6 slices of pizza and paid $6.70. Amy bought 4 slices of pizza and 3 drinks and paid $4.65. What price is each drink and each slice of pizza?

6. Students pay $2 per ticket and adults pay $5 per ticket. The stadium is filled to its capacity of 2000, however, 254 of those seats are given free of charge to band members, pep squad members, and faculty members. The ticket-booth manager reports to the athletic director that the total income from the sale of tickets for the current game is $5766. How many student and adult tickets were sold?

7. A father is 28 years older than his son. In 5 years the father will be 5 times as old as his son. How old is each now?

8. Becky is 10 years older than Michael. Four years ago, Becky was twice as old as Michael. How old is each now?

9. The sum of two numbers is 17. The smaller number is 33 less than the greater number. Find the two numbers.

10. An exam worth 145 points contains 50 questions. Some of the questions are worth two points and some are worth five points. How many two-point questions are on the test? How many five-point questions are on the test?

  1. A class of 195 students went on a field trip. They took 7 vehicles, some cars and some buses. Find the number of cars and the number of buses they took if each car holds 5 students and each bus holds 45 students.

Graph each of the following systems and then determine if they are independent, dependent, or inconsistent.

12. y = -2x + 313. y = 1/2x – 3

-8x – 4y = 20 3x – 2y = 10