Conquer Linear Systems: Mastering Elimination!

Algebra 2 Grades High School 12:40 Video
Print Lesson Plan Watch Video

Lesson Description

Learn how to solve systems of linear equations using the elimination method. This lesson covers organizing equations, identifying matching coefficients, and strategically adding or subtracting to eliminate variables. Perfect for Algebra 2 students!

Video Resource

Solve Linear Systems Elimination

Kevinmathscience

Duration: 12:40
Watch on YouTube

Key Concepts

  • Systems of linear equations
  • Elimination method
  • Coefficient matching
  • Strategic addition/subtraction

Learning Objectives

  • Students will be able to rearrange linear equations into a standard form (Ax + By = C).
  • Students will be able to identify when to add or subtract equations to eliminate a variable.
  • Students will be able to solve for one variable using the elimination method.
  • Students will be able to substitute the solved variable back into an original equation to find the other variable.
  • Students will be able to identify the solution to a system of equations as an ordered pair (x, y).

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing what a system of linear equations represents (two or more lines intersecting at a point). Briefly discuss the graphing method and introduce the elimination method as an alternative approach that doesn't require graphing. Show the video from Kevinmathscience, Solve Linear Systems Elimination.
  • Step 1: Organize Equations (10 mins)
    Explain the importance of having equations in the standard form (Ax + By = C). Provide examples and guide students through rearranging equations to match this form. Emphasize that the X term needs to be first and the constant should be on the right side of the equal sign.
  • Step 2: Identify Matching Coefficients (10 mins)
    Discuss how to identify matching or near-matching coefficients for either x or y. Explain that 'near-matching' means that with a simple multiplication, coefficients can become the same. Work through examples where coefficients are already the same and examples where one or both equations need to be multiplied by a constant.
  • Step 3: Eliminate a Variable (15 mins)
    Explain the core concept of the elimination method: adding or subtracting equations to eliminate one variable. Provide rules for when to add (opposite signs) and when to subtract (same signs). Work through several examples, clearly showing each step of the addition/subtraction process. Stress the importance of distributing the negative sign correctly when subtracting equations.
  • Step 4: Solve for the Remaining Variable (5 mins)
    Once a variable is eliminated, explain how to solve for the remaining variable using basic algebraic principles (division). Work through examples.
  • Step 5: Substitute and Solve (10 mins)
    Show students how to substitute the value of the solved variable back into one of the original equations to find the value of the other variable. Emphasize that either original equation can be used and will yield the same result. Work through examples.
  • Practice and Wrap-up (15 mins)
    Provide students with practice problems to work on individually or in pairs. Circulate to provide assistance. Review the solutions and answer any remaining questions. Summarize the steps of the elimination method.

Interactive Exercises

  • Equation Sort
    Provide students with a set of equations, some in standard form and some not. Have them sort the equations into two groups.
  • Elimination Challenge
    Present students with systems of equations and challenge them to identify the easiest variable to eliminate and the correct operation (addition or subtraction).

Discussion Questions

  • Why is it important to have the equations in the standard form before applying the elimination method?
  • How do you decide whether to add or subtract the equations?
  • What happens if you make a mistake when distributing the negative sign during subtraction?
  • If you multiply one equation by a number, do you have to multiply the other one as well?

Skills Developed

  • Algebraic manipulation
  • Problem-solving
  • Critical thinking
  • Attention to detail

Multiple Choice Questions

Question 1:

What is the first step in solving a system of equations using the elimination method, according to the video?

Correct Answer: Getting x and y on the left side of the equation

Question 2:

When should you ADD the equations in the elimination method?

Correct Answer: When the coefficients of either x or y are opposites

Question 3:

If you solve for 'y' using elimination, what is the next step to find 'x'?

Correct Answer: Substitute the value of 'y' into one of the original equations

Question 4:

In the elimination method, what does it mean to 'eliminate' a variable?

Correct Answer: To make the variable equal to zero

Question 5:

When is it necessary to multiply one or both equations by a constant in the elimination method?

Correct Answer: When the coefficients of x or y are not the same, or multiples of each other

Question 6:

Consider the system: 2x + y = 5 and 4x - y = 1. What happens when you add the two equations?

Correct Answer: The y variable is eliminated

Question 7:

Which of the following is the standard form for a linear equation used in the elimination method?

Correct Answer: Ax + By = C

Question 8:

When subtracting equations in the elimination method, what must you remember to do?

Correct Answer: Distribute the negative sign to all terms in the equation being subtracted

Question 9:

What does the solution to a system of linear equations represent?

Correct Answer: The point where the two lines intersect

Question 10:

What is the solution to the following system of equations? x + y = 5 and x - y = 1

Correct Answer: (3, 2)

Fill in the Blank Questions

Question 1:

The method discussed in the video for solving systems of equations without graphing is called __________.

Correct Answer: elimination

Question 2:

Before eliminating, you should get X and Y on the _____ side of the equation.

Correct Answer: left

Question 3:

When using the elimination method, if the coefficients of a variable are opposites, you should ______ the equations.

Correct Answer: add

Question 4:

When using the elimination method, if the coefficients of a variable are the same, you should ______ the equations.

Correct Answer: subtract

Question 5:

The solution to a system of linear equations is written as an ___________.

Correct Answer: ordered pair

Question 6:

When subtracting equations, you must remember to ______ the negative sign.

Correct Answer: distribute

Question 7:

If neither the x nor y coefficients match, you will need to find the ____________ to solve the problem.

Correct Answer: lowest common multiple

Question 8:

The overall goal of the elimination method is to _______ one of the variables

Correct Answer: eliminate

Question 9:

The solution of a system of linear equations represents the point of ________ of the two lines

Correct Answer: intersection

Question 10:

When a variable has been eliminated, the resulting equation will contain only _______ variable.

Correct Answer: one

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

Download ready-to-use materials for this lesson:

Student Worksheet Classroom Slides Assessment Quiz Export to Google Docs
Add to Google Classroom

User Actions

Sign in to save this lesson plan to your favorites.

Sign In

Share This Lesson

Related Lesson Plans