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Algebra 2 3-5 Complete Lesson: Systems With Three Variables

Last updated almost 4 years ago
22 questions
Note from the author:
A complete formative lesson with embedded slideshow, mini lecture screencasts, checks for understanding, practice items, mixed review, and reflection. I create these assignments to supplement each lesson of Pearson's Common Core Edition Algebra 1, Algebra 2, and Geometry courses. See also mathquest.net and twitter.com/mathquestEDU.
Solve It! How much does each box weigh?
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Drag and drop to identify the mass of each box.

  • 1 lb
  • 2 lb
  • 3 lb
  • 4 lb
  • 5 lb
  • 6 lb
  • A Boxes
  • B Boxes
  • C Boxes
10

Problem 1 Got It?

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Problem 2 Got It? What is the solution of the system? Use elimination.

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Problem 2 Got It? Reasoning: Could you have used elimination in another way? Explain. HINT: Could you have eliminated a difference variable first?

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Problem 3 Got It? What is the solution of the system? Use substitution.

  • -4
  • -2
  • 0
  • 1
  • 2
  • 4
  • x =
  • y =
  • z =
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Problem 4 Got It?

10
10
10
10
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Reasoning: How do you decide whether substitution is the best method to solve a system in three variables?

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Error Analysis: A classmate says that the system consisting of x = 0, y = 0, and z = 0 has no solution. Explain the student's error.

10

Writing: How many solutions does this system have? Hint: Is the system dependent? inconsistent?
Explain your answer in terms of intersecting planes.

10

Visualize: The graph of a system is shown here. How many solutions does this system have? Explain.

10

Review Lesson 3-4:
1. Graph the system of inequalities to form a feasible region.
2. Zoom and pan your graph to establish an appropriate viewing window.
3. Click on each vertex of the feasible region to make its label appear.
4. Re-zoom and re-pan again, if necessary, to ensure that the feasible region and vertex labels are showing.

10

Review Lesson 3-4: Refer to the constraints and feasible region in the previous item. At what vertex does the maximum value occur for the objective function, P, below?

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Review Lesson 1-5: Solve the inequality. Graph the solution on a number line.

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Review Lesson 3-2: Solve the system using elimination. Show your work on the canvas and write the solution in the space provided.

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Vocabulary Review: How many points determine a plane?

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Use Your Vocabulary: Classify each ordered triple based on its x-coordinate.

  • (1, 0, 1)
  • (1, 1, 0)
  • (0, 1, 1)
  • (1, 0, 0)
  • Has x-coordinate 0
  • Has x-coordinate 1
100

Notes: Take a clear picture or screenshot of your Cornell notes for this lesson. Upload it to the canvas. Zoom and pan as needed.

For a refresher on the Cornell note-taking system, click here.

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Reflection: Math Success