MATH Integrated Math I  - Unit 33: Systems of Equations: Elimination
Some of the questions in this unit may be answered by recording an audio file. If you chose to record the answer, click on the Add Recording button and follow the on-screen instructions closely. Once you have completed and attached the recording, enter the word “COMPLETE” in the text box. (Note: If your computer does not have a built-in microphone, a microphone or microphone/headset combination is needed to record audio.) Review

The lines of several equations are graphed below. Refer to these lines to solve the next four problems.  Click to view the graph of the lines in a pop-up window.

1) Does the system of equations represented by line “l” and line “k” have “one” solution, “no” solution, or many solutions? If the system has one solution, state the ordered pair for the solution.

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2) Does the system of equations represented by line “m” and line “n” have “one” solution, “no” solution, or many solutions? If the system has one solution, state the ordered pair for the solution.

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3) Does the system of equations represented by line “n” and line “k” have “one” solution, “no” solution, or many solutions? If the system has one solution, state the ordered pair for the solution.

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4) Does the system of equations represented by line “k” and line “m” have “one” solution, “no” solution, or many solutions? If the system has one solution, state the ordered pair for the solution.

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For the next four problems, solve each system as directed. State the solution as an ordered pair. There is a link to graph paper in the content area of this unit.

5) Solve the system by graphing.

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6) Solve the system by graphing.

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7) Solve the system by substitution.

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8) Solve the system by substitution.

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The Elimination Method

9) Explain the process of using elimination to solve a system of equations. 

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For the next five problems, use the process of elimination to solve the system of equations.

10) Solve the system of equations by elimination.

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11) Explain the solution to the previous problem.

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12) Solve the system of equations by elimination.

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13) Solve the system of equations by elimination.

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14) Solve the system of equations by elimination.

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 Consistent and Inconsistent Systems

15) What is the difference between a consistent and an inconsistent system of equations?

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For the next three problems, solve the system, and then determine if the system is consistent or inconsistent.  If the system has a solution, state the solution as an ordered pair.

16) What is the solution of the system? Is the system consistent or inconsistent?

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17) What is the solution of the system? Is the system consistent or inconsistent?

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18) What is the solution of the system? Is the system consistent or inconsistent?

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Independent and Dependent Systems

19) What is the difference between a dependent and an independent system of equations?

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For the next three problems, solve the system, and then determine if the system is a dependent or an independent system. If the system has a solution, state the solution as an ordered pair.

20) What is the solution of the system? Is the system dependent or independent?

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21) What is the solution of the system? Is the system dependent or independent?

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22) What is the solution of the system? Is the system dependent or independent?

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Applications

Refer to the following scenario to answer the next two questions: The band has a total of 22 majorettes and flag twirlers. There are 6 more flag twirlers than there are majorettes. How many majorettes and flag twirlers are in the club?

23) For the given scenario, (1) define each of the variables and (b) state a system of equations that can be used to solve the problem. 

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24) What is the solution for the system of equations?

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Refer to the following scenario to answer the next three questions: While shopping at a local warehouse club, Mary bought her children one game box and four video games (all priced the same) which totaled $167. The next day she returned to the club to buy two more game boxes and five more video games for $283. What is the price of each game box and each video game?

25) For the given scenario, (1) define each of the variables and (b) state a system of equations that can be used to solve the problem. 

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26) What is the solution for the system of equations?

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For the next two problems, set up a system of equations for the given scenario, and then solve the problem.

27) To attend Lakewood High's football game, an adult ticket costs $7 and a student ticket costs $3. There were 175 tickets sold at the game. If the ticket sales totaled $777, how many adult tickets and how many student tickets were sold at the game?

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28) The Country Inn offers mini vacation packages. One vacation package includes a stay of 4 nights and 8 meals for $299. A second vacation package includes a stay of 2 nights and 6 meals for $174. What are the room rate and the cost of each meal?

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Choosing a Method for Solving Systems

For the last five problems, select one of the three methods (graphing, substitution, or elimination) for solving systems of equations, and then solve.

29) For the given system of equations, (a) what method was used to solve the system of equations and (b) what is the ordered pair that represents the solution to the system of equations? 

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30) For the given system of equations, (a) what method was used to solve the system of equations and (b) what is the ordered pair that represents the solution to the system of equations

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31) For the given system of equations, (a) what method was used to solve the system of equations and (b) what is the ordered pair that represents the solution to the system of equations? 

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32) For the given system of equations, (a) what method was used to solve the system of equations and (b) what is the ordered pair that represents the solution to the system of equations? 

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33) For the given system of equations, (a) what method was used to solve the system of equations and (b) what is the ordered pair that represents the solution to the system of equations? 

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