Conquer Systems of Equations: The Elimination Method

Algebra 2 Grades High School 11:21 Video
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Lesson Description

Master the elimination method to solve systems of equations. Learn to add, subtract, and multiply equations to eliminate variables and find solutions. Explore special cases like infinite solutions and no solution.

Video Resource

Elimination Method for Solving Systems of Equations Addition & Subtraction

Mario's Math Tutoring

Duration: 11:21
Watch on YouTube

Key Concepts

  • Systems of Equations
  • Elimination Method (Addition/Subtraction)
  • Multiplying Equations by a Constant
  • Infinite Solutions
  • No Solution

Learning Objectives

  • Students will be able to solve systems of equations using the elimination method.
  • Students will be able to identify and solve systems of equations that result in infinite solutions or no solution.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the concept of systems of equations and their graphical representation (lines intersecting at a point). Briefly discuss other methods for solving systems, such as substitution, and introduce the elimination method as a new technique.
  • Video Presentation (15 mins)
    Play the "Elimination Method for Solving Systems of Equations Addition & Subtraction" video by Mario's Math Tutoring. Instruct students to take notes on the different examples presented, focusing on the steps involved in each case.
  • Guided Practice (20 mins)
    Work through the examples from the video on the board, pausing to explain each step in detail and answer student questions. Emphasize the importance of checking solutions by substituting them back into the original equations. Also show how multiplying by the lowest common multiple makes solving equations easier.
  • Independent Practice (15 mins)
    Provide students with a set of practice problems to solve independently using the elimination method. Circulate the classroom to provide assistance as needed.
  • Wrap-up and Discussion (5 mins)
    Review the key concepts of the elimination method and address any remaining questions. Discuss the advantages and disadvantages of using the elimination method compared to other methods.

Interactive Exercises

  • Error Analysis
    Present students with worked-out problems that contain errors. Ask them to identify the errors and correct them.
  • System Solver Challenge
    Divide the class into groups and give each group a challenging system of equations to solve. The first group to correctly solve the system wins.

Discussion Questions

  • When is the elimination method the most efficient way to solve a system of equations?
  • How do you know when a system of equations has infinite solutions or no solution when using the elimination method?
  • Can you use elimination method with three variables? What modifications would need to be made?

Skills Developed

  • Algebraic Manipulation
  • Problem-Solving
  • Critical Thinking

Multiple Choice Questions

Question 1:

Which operation is used in the elimination method to get rid of one of the variables in a system of equations?

Correct Answer: Addition/Subtraction

Question 2:

What does it mean if, after applying the elimination method, you get 0 = 0?

Correct Answer: Infinitely many solutions

Question 3:

In the system: x + y = 5 and 2x - y = 1, what is the value of x after eliminating y by adding the equations?

Correct Answer: x = 2

Question 4:

When multiplying an equation by a constant in the elimination method, which part(s) of the equation must be multiplied?

Correct Answer: Both sides

Question 5:

Which of the following systems of equations would be best solved using elimination (without needing to multiply)?

Correct Answer: x + y = 4 and x - y = 2

Question 6:

What does it mean graphically when a system of equations has infinitely many solutions?

Correct Answer: The lines are the same

Question 7:

If you get 0 = 1 after eliminating a variable, what does this indicate about the system of equations?

Correct Answer: No solution

Question 8:

To eliminate 'x' from the following system: 2x + 3y = 7 and x + 4y = 9, by what should the second equation be multiplied?

Correct Answer: -2

Question 9:

In the elimination method, why is it sometimes necessary to multiply one or both equations by a constant?

Correct Answer: To make the coefficients of one variable opposites

Question 10:

What is the first step in solving the following system of equations using elimination: 3x + 2y = 8 and 5x - 2y = 4?

Correct Answer: Add the equations

Fill in the Blank Questions

Question 1:

The __________ method involves adding or subtracting equations to eliminate a variable.

Correct Answer: elimination

Question 2:

If the elimination method results in 0 = 5, the system has __________.

Correct Answer: no solution

Question 3:

When using the elimination method, it is important to check your __________ by plugging them back into the original equations.

Correct Answer: solution

Question 4:

If eliminating variables results in 0 = 0, the system has __________ solutions.

Correct Answer: infinite

Question 5:

Before adding or subtracting, you may need to __________ one or both equations by a constant.

Correct Answer: multiply

Question 6:

The point where two lines intersect is called the _________.

Correct Answer: solution

Question 7:

The coefficients of the variable you want to eliminate must be _______ for adding to work.

Correct Answer: opposites

Question 8:

Before eliminating, ensure variables are _______ in columns.

Correct Answer: aligned

Question 9:

A system of equations represents two or more ______.

Correct Answer: equations

Question 10:

After solving for one variable, you must ______ it back into one of the original equations to solve for the other.

Correct Answer: substitute

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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