Module 7: Lesson 4

Module 7: Systems of Linear Equations

Connect
Lesson Assessment

Complete the lesson quiz posted under the Quizzes link to the left in moodle or under the Assess tab and ensure your work in your binder (course folder) is complete.Β 
Update your Strategies for Solving Linear Systems page at this time as well.

Project Connection **NOT ASSIGNED**

This photo shows a woman trying on running shoes in a shoe store. She is being assisted by a store employee.

Digital/Vision/Photodisc/Thinkstock

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Throughout the Unit 4 Project, you have been asked questions related to taking a vacation. Now imagine that you are taking your vacation. During a break in your itinerary, you decide to go shopping at the local outlet mall where brand-name stores sell last season’s fashions at discounted prices. At a particular shoe store, there is a sale where you can buy one pair and get the second pair for half price. In cases where the two pairs are of unequal value, the discount applies to the less expensive pair. For example, if one pair was $100 and the second pair was $60, then you would only receive the 50% discount on the $60 pair.

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Now go to the Unit 4 Project, and complete the Module 7: Lesson 4 component of the project.

Going Beyond

You have previously considered the solution to a system of three equations in three variables. In this lesson you learned how to solve a linear system by elimination. You can solve a system of three equations in three variables by using the same method. In the Going Beyond section in Lesson 1, you explored how you might graph each equation in the following system.

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x + y + z = 6

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2x βˆ’ y + z = 3

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x + y βˆ’ z = 0

  1. You can now use elimination to solve this same system of equations. Follow the steps below to find the values of x, y, and z that will satisfy the system.

    1. Choose two of the three equations. Use the elimination method to eliminate one of the variables. Call the resulting expression Equation A.
    2. Now choose a different pair of the original equations. One of the equations will be the same as in the first pair. Use the elimination method to eliminate the same variable as in step 2. Call the resulting expression Equation B.
    3. You should now have two equations with two variables. Solve the linear system represented by Equation A and Equation B.
    4. Use the values of the variables found in step 2 to determine the value of the third variable.
Reflect on the following questions.
  1. How many other ways could you have solved this question using elimination?
  2. How can you verify your solution?
  3. How would you verify your solution with the online matrix calculator?

Save your work in your course folder.

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