Conquering Systems of 3 Equations with Elimination
Lesson Description
Video Resource
Key Concepts
- Elimination Method
- Systems of Equations
- Variable Isolation
- Solution Triple (x, y, z)
Learning Objectives
- Students will be able to identify the easiest variable to eliminate in a system of three equations.
- Students will be able to apply the elimination method to reduce a system of three equations to a system of two equations.
- Students will be able to solve for all three variables in a system of three equations using back-substitution.
Educator Instructions
- Introduction (5 mins)
Briefly review systems of two equations with two variables and the elimination method. Explain how systems of three equations represent planes in 3D space (as mentioned in the video description). - Video Presentation (10 mins)
Play the 'Solving Systems of 3 Equations Elimination' video by Mario's Math Tutoring. Encourage students to take notes on the steps involved. - Step-by-Step Walkthrough (15 mins)
Work through the example from the video on the board, explaining each step in detail. Emphasize the importance of choosing the easiest variable to eliminate and being careful with algebraic manipulations. Highlight that the equations represent planes. - Practice Problems (15 mins)
Provide students with practice problems to solve independently or in small groups. Circulate to provide assistance and answer questions. - Review and Q&A (5 mins)
Review the solutions to the practice problems and answer any remaining questions from the students.
Interactive Exercises
- Group Elimination Challenge
Divide the class into small groups and assign each group a different system of three equations. Challenge them to solve the system using elimination within a set time limit. The first group to correctly solve their system wins. - Error Analysis
Present students with a worked-out solution to a system of equations that contains an error. Ask them to identify the error and explain how to correct it.
Discussion Questions
- Why is it important to use all three equations when solving a system of three equations using elimination?
- What are some strategies for choosing the easiest variable to eliminate?
- How can you check your solution to ensure it is correct?
Skills Developed
- Algebraic Manipulation
- Problem-Solving
- Critical Thinking
- Strategic Planning
Multiple Choice Questions
Question 1:
When using the elimination method for a system of three equations, what is the first goal?
Correct Answer: Eliminate one variable.
Question 2:
Which operation is commonly used in the elimination method to cancel out a variable?
Correct Answer: Addition or Subtraction
Question 3:
After eliminating one variable from two pairs of equations, what type of system are you left with?
Correct Answer: A system of two equations with two variables.
Question 4:
What does the solution to a system of three equations with three variables represent graphically?
Correct Answer: A point of intersection of three planes.
Question 5:
What is the final step in solving a system of three equations after finding the value of one variable?
Correct Answer: Back-substitution.
Question 6:
If you multiply an equation by a constant during elimination, what must you do to the entire equation?
Correct Answer: Multiply every term on both sides of the equation.
Question 7:
When checking your solution (x, y, z), how many of the original equations must it satisfy?
Correct Answer: All three.
Question 8:
What is the solution to a system of three equations called?
Correct Answer: A triple
Question 9:
Why do we pick the 'easiest' variable to eliminate?
Correct Answer: To minimize errors
Question 10:
What does the video suggest about which variables you choose to eliminate first?
Correct Answer: You can choose based on what looks easiest
Fill in the Blank Questions
Question 1:
The method demonstrated in the video to solve the systems of equation is called the _______ method.
Correct Answer: elimination
Question 2:
When choosing a variable to eliminate, select the one that appears _______ to cancel out.
Correct Answer: easiest
Question 3:
After eliminating one variable, you're left with a system of two equations with two _______.
Correct Answer: variables
Question 4:
The process of substituting known values back into previous equations is called _______-substitution.
Correct Answer: back
Question 5:
The solution to a system of three equations is written as an ordered _______ (x, y, z).
Correct Answer: triple
Question 6:
Each equation in a system of three variables represents a _______ in three-dimensional space.
Correct Answer: plane
Question 7:
To eliminate a variable, you often need to _______ one or more equations by a constant.
Correct Answer: multiply
Question 8:
The intersection of three planes represents the _______ to a system of three equations.
Correct Answer: solution
Question 9:
After finding the values of x and y, you _______ these values into one of the original equations to find z.
Correct Answer: substitute
Question 10:
In the elimination method, you want to reduce the system to a single equation with one _______.
Correct Answer: variable
Educational Standards
Teaching Materials
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