Conquering 3x3 Systems: Substitution in Action!

Algebra 2 Grades High School 16:08 Video
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Lesson Description

Master the substitution method to solve systems of three equations with three variables. This lesson builds on prior knowledge of two-variable systems and extends it to the more complex 3x3 case.

Video Resource

Solving Systems of Equations with Three Variables Algebra | Substitution

Kevinmathscience

Duration: 16:08
Watch on YouTube

Key Concepts

  • Systems of Equations
  • Substitution Method
  • Variable Isolation

Learning Objectives

  • Students will be able to isolate a variable in a three-variable equation.
  • Students will be able to apply the substitution method to solve a system of three equations with three variables.
  • Students will be able to check their solutions by substituting the values back into the original equations.

Educator Instructions

  • Introduction (5 mins)
    Briefly review solving systems of equations with two variables using substitution. Emphasize the goal: to reduce a 3-variable system to a series of 2-variable systems.
  • Video Viewing (15 mins)
    Watch the 'Solving Systems of Equations with Three Variables Algebra | Substitution' video by Kevinmathscience. Encourage students to take notes on the steps involved in the substitution method.
  • Guided Practice (20 mins)
    Work through example problems on the board, demonstrating each step of the substitution method. Encourage students to participate and ask questions. Follow the examples from the video, breaking them down further.
  • Independent Practice (20 mins)
    Assign practice problems for students to solve individually. Circulate to provide assistance as needed. Offer a mix of problems with varying difficulty levels.
  • Wrap-up (5 mins)
    Review the key steps of the substitution method. Answer any remaining questions. Preview the upcoming lesson on solving systems of equations using other methods.

Interactive Exercises

  • Group Problem Solving
    Divide students into small groups and assign each group a challenging system of equations to solve using substitution. Have each group present their solution to the class.
  • Error Analysis
    Present students with a worked-out solution to a system of equations that contains an error. Have them identify the error and correct it.

Discussion Questions

  • What are the advantages and disadvantages of using the substitution method compared to elimination?
  • In what types of systems of equations might substitution be the preferred method?
  • How can you check your solutions to ensure they are correct?

Skills Developed

  • Algebraic Manipulation
  • Problem-Solving
  • Critical Thinking

Multiple Choice Questions

Question 1:

What is the first step in solving a 3x3 system of equations using substitution?

Correct Answer: Isolate one variable in one of the equations.

Question 2:

After isolating a variable, what do you do next?

Correct Answer: Substitute the expression into the other equations.

Question 3:

When can you use elimination to solve the equations?

Correct Answer: After substitution

Question 4:

What indicates that a solution is extraneous?

Correct Answer: The solution does not satisfy all original equations.

Question 5:

In a 3x3 system, how many variables should you have isolated before substituting?

Correct Answer: 1

Question 6:

What does it mean when we say that one variable is 'by itself'?

Correct Answer: The variable is isolated on one side of the equation.

Question 7:

Which method is an alternative for solving the system of equations?

Correct Answer: Elimination

Question 8:

What are the variables in the system of equations?

Correct Answer: r, t, s

Question 9:

How do you solve for the third variable?

Correct Answer: Solve using all of the previous solutions

Question 10:

What is an alternate way to represent the solution set to a system of three equations?

Correct Answer: Matrix

Fill in the Blank Questions

Question 1:

The goal of substitution is to reduce a 3-variable system to a series of ______ systems.

Correct Answer: 2-variable

Question 2:

When checking your solution, the values must satisfy ______ original equations.

Correct Answer: all

Question 3:

After substituting the first isolated variable, you will have a new system with ______ variables.

Correct Answer: two

Question 4:

If you isolate 'x' in one equation, you should substitute it into the other equations, but not the equation where you ______ x.

Correct Answer: isolated

Question 5:

Before you can substitute, you need to isolate one ______.

Correct Answer: variable

Question 6:

After you have two equations with two variables, you must isolate one of the ______.

Correct Answer: variables

Question 7:

The video offers _______ to label the equations

Correct Answer: number

Question 8:

Remember to check _______ with the new values.

Correct Answer: work

Question 9:

Remember to write the solution in _______ order.

Correct Answer: alphabetical

Question 10:

After the first variable is isolated, then substitute into _______ equations.

Correct Answer: all

Educational Standards

A2.A.1.7:Represent and evaluate mathematical models using systems of linear equations with a maximum of three variables. Graphing calculators or other appropriate technology may be used. A2.A.2:Generate and evaluate equivalent algebraic expressions and equations using various strategies.

Teaching Materials

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