Conquering 3x3 Systems: Elimination Domination!

Algebra 2 Grades High School 24:05 Video
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Lesson Description

Master the elimination method to solve systems of equations with three variables. Reduce the system to two variables and then solve!

Video Resource

Solving Systems of Equations with Three Variables Algebra | Elimination

Kevinmathscience

Duration: 24:05
Watch on YouTube

Key Concepts

  • Systems of equations with three variables
  • Elimination method
  • Reducing a 3-variable system to a 2-variable system

Learning Objectives

  • Students will be able to identify a system of equations with three variables.
  • Students will be able to use the elimination method to reduce a 3-variable system to a 2-variable system.
  • Students will be able to solve a system of equations with three variables using the elimination method.

Educator Instructions

  • Introduction (5 mins)
    Briefly review solving systems of equations with two variables (graphing, elimination, substitution). Introduce the concept of systems with three variables (x, y, z) and explain that we'll focus on the elimination method to solve these.
  • Video Viewing and Note-Taking (20 mins)
    Play the Kevinmathscience video 'Solving Systems of Equations with Three Variables Algebra | Elimination'. Instruct students to take notes on the steps involved in the elimination method, focusing on how to choose which variable to eliminate and how to combine equations.
  • Guided Practice (25 mins)
    Work through example problems on the board, demonstrating the elimination method step-by-step. Emphasize choosing a variable to eliminate, combining equations to eliminate the chosen variable, solving the resulting 2-variable system, and back-substituting to find all three variables. Have students work along with you, solving each step in their notebooks.
  • Independent Practice (20 mins)
    Provide students with a worksheet containing systems of equations with three variables. Have them work independently to solve the systems using the elimination method. Circulate to provide assistance and answer questions.
  • Wrap-up and Assessment (10 mins)
    Review the key steps of solving systems of equations with three variables using elimination. Assign a short multiple choice and fill in the blank quiz to assess student understanding.

Interactive Exercises

  • Equation Combination Challenge
    Present students with a system of three equations and ask them, in small groups, to determine the best way to combine the equations to eliminate a specific variable. Have them share their strategies and explain their reasoning.

Discussion Questions

  • Why is it important to eliminate the same variable in each pair of equations?
  • What are some strategies for choosing which variable to eliminate first?
  • How does the elimination method for 3-variable systems relate to the elimination method for 2-variable systems?

Skills Developed

  • Algebraic manipulation
  • Problem-solving
  • Logical reasoning

Multiple Choice Questions

Question 1:

Which method is primarily taught in the video for solving systems of three equations?

Correct Answer: Elimination

Question 2:

What is the first step in solving a 3x3 system using elimination?

Correct Answer: Eliminating one variable from two equations

Question 3:

When eliminating a variable, why must you eliminate the SAME variable from BOTH pairs of equations you choose?

Correct Answer: To ensure consistency and obtain a 2x2 system

Question 4:

After reducing the 3x3 system to a 2x2 system, what do you do?

Correct Answer: Solve the 2x2 system using elimination or substitution

Question 5:

Once you solve the 2x2 system, how do you find the value of the third variable?

Correct Answer: Back-substitute the known values into one of the original equations

Question 6:

In the example problems, what is the goal of multiplying one or both equations by a constant?

Correct Answer: To make the coefficients of a variable opposites or equal

Question 7:

If you choose to eliminate 'x' first, which variable must you eliminate when working with a different pair of equations from the original set?

Correct Answer: x

Question 8:

What is the benefit of eliminating variables in a system of equations?

Correct Answer: It simplifies the system to be more easily solved

Question 9:

What should you do with equations, if after combining your equations all variables are eliminated and you get a false statement (ex. 0=1)?

Correct Answer: The system is inconsistant and the equation has no solution.

Question 10:

When back-substituting, which equation is best for finding all the variables.

Correct Answer: Any of the original equations will work.

Fill in the Blank Questions

Question 1:

The primary method taught in the video for solving systems of three variables is the __________ method.

Correct Answer: elimination

Question 2:

When using the elimination method, the goal is to reduce the 3-variable system to a __-variable system.

Correct Answer: 2

Question 3:

To eliminate a variable, you may need to __________ one or both equations by a constant.

Correct Answer: multiply

Question 4:

After solving the reduced system, you must __________ to find the value of the remaining variable(s).

Correct Answer: back-substitute

Question 5:

When choosing which variable to eliminate, it is important to eliminate the __________ variable from both pairs of equations you choose.

Correct Answer: same

Question 6:

The solution to a system of equations with three variables is a(n) __________ triple.

Correct Answer: ordered

Question 7:

If you eliminate one variable, and the other variables are eliminated also, and it leads to a true answer, such as 0=0, the solution to the system of equations is __________.

Correct Answer: infinite

Question 8:

If the final result shows a situation with two parallel lines that do not intersect, there will be __________ solutions for the system of equations.

Correct Answer: no

Question 9:

If you are inconsistent and eliminate a different variable in the second step than you did in the first step of solving a system of equations, the result will be __________.

Correct Answer: incorrect

Question 10:

After multiplying a system of equations, you will either need to add the equations together, or __________ the equations from each other.

Correct Answer: subtract

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.

Teaching Materials

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