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

Last updated about 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.

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

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

Problem 1 Got It?

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

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

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

Problem 4 Got It?

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

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.

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

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

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?

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

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

Vocabulary Review: How many points determine a plane?

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

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.

Reflection: Math Success

Drag and drop to identify the mass of each box.

Problem 1 Got It?

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

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

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

Problem 4 Got It?

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

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.

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

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

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?

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

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

Vocabulary Review: How many points determine a plane?

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

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.

Reflection: Math Success

Drag and drop to identify the mass of each box.

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

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

Problem 1 Got It?

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

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

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

Problem 4 Got It?

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

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.

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

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

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?

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

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

Vocabulary Review: How many points determine a plane?

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

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.

Reflection: Math Success

Drag and drop to identify the mass of each box.

Problem 1 Got It?

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

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

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

Problem 4 Got It?

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

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.

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

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

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?

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

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

Vocabulary Review: How many points determine a plane?

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

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.

Reflection: Math Success

Drag and drop to identify the mass of each box.

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

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.

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

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.