Simultaneous Equations Lesson Plan

Instructor: Maria Airth

Maria has a Doctorate of Education and over 15 years of experience teaching psychology and math related courses at the university level.

This lesson plan helps teachers instruct students on the different methods for solving simultaneous equations. Students are presented with video instruction leading to an engaging game in which to practice the skills learned.

Learning Objectives

After this lesson, students will be able to:

  • Demonstrate multiple methods of solving simultaneous equations
  • Define ''simultaneous equations''
  • Identify logical reasoning for choosing one method of solution over another


30-90 minutes

Curriculum Standards


Analyze and solve pairs of simultaneous linear equations.


Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.


Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 8 topics, texts, and issues, building on others' ideas and expressing their own clearly.


  • Copies of the transcript of the video lesson How to Solve Simultaneous Equations and hard copies of the lesson quiz
  • Audio/video equipment
  • Prepared list of simultaneous equations that have solutions and others that do not have solutions

Warm-Up Activity

  • Review the concept of solving an equation with an example on the board. Write any simple (x, y) linear equation on the board and ask your students to graph it using:
    • The slope/intercept method
    • Substitution of values chart
  • Allow volunteers to show each solution on the board.
  • Now, ask your students to identify the value of y given a specific value of x (you choose the value).
  • Discuss the difficulty level of this exercise. Ask your students if it would be more difficult if they had to work on two equations at once instead of just one.
  • Tell your students that this scenario is exactly what today's lesson is about.
  • Ask your students to prepare to take notes on the following video lesson.


  • Play the video straight through.
  • Afterward, write two relatively simple equations on the board. You could use:
    • 4x + 3y = 2
    • 2x - 3y = 10
  • Now, tell your students that you will be re-playing the video with pauses throughout so that they can work out the solution to the system of equations you have written on the board using the methods shown in the video.
  • Hand out the transcripts before restarting the video.
  • Instruct your students to highlight/underline the important definitions as you reach them in the video.
  • Pause at the following time markers to allow students time to solve your given system of equations after a review of each method. Remind your students to show their work on each method.
    • Graphing: 1:30
    • Elimination: 5:12
    • Substitution: 8:35 (must solve for any variable first)
  • After each method, allow a student to go to the board and work through the solution for the class.
  • Allow time for questions and working through additional examples of each method, if required. Refer to your prepared list of simultaneous equations, if needed.
  • Before replaying the 'No Solution' section of the video (time marker 8:35), give a few examples of simultaneous equations that do not have solutions and ask your students to write down why each does not have a solution. For example, they may be parallel or the same graph.
  • Finish the video.
  • Instruct your students to review their transcripts and notes and ask any questions they may have before the quiz.
  • Hand out the lesson quiz. Go over each question and answer with the class after they have finished it.

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