ChalkHour

Year 9 Maths: Simultaneous equations lesson pack

A complete, ready-to-teach KS3 lesson on simultaneous equations. Below is a real sample of what ChalkHour makes: the full pack adds three levels of worksheet, model answers, a teaching explainer and print-ready PDF and Word files.

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Real sample

Solving Linear Simultaneous Equations by Elimination

A comprehensive lesson on solving linear simultaneous equations using the elimination method, moving from basic addition/subtraction to scaling equations and solving worded problems.

Learning objectives

  • Solve linear simultaneous equations by elimination where coefficients of one variable are the same.
  • Solve linear simultaneous equations where one or both equations must be multiplied to match coefficients.
  • Set up and solve simultaneous equations from worded real-world problems.

Lesson plan (60 minutes)

  1. Introduction · 10 min

    Starter: Retrieval of solving linear equations and basic substitution.

  2. Teaching · 15 min

    Direct Instruction: Explaining the elimination method for equations with same coefficients.

  3. Guided Practice · 10 min

    Guided Practice: Solving two examples together on mini-whiteboards.

  4. Independent Practice · 20 min

    Independent Practice: Differentiated worksheets (Support, Core, Stretch).

  5. Review · 5 min

    Plenary: Multiple-choice quiz to check for misconceptions.

Key vocabulary

Simultaneous Equations
Equations that are true at the same time and share the same variables.
Coefficient
The number in front of a variable (e.g., in 4x, 4 is the coefficient).
Elimination
The process of removing one variable by adding or subtracting equations.
Substitution
Replacing a variable with a specific value or expression.
Constant
A value in an equation that does not change (the number without a letter).

Core worksheet (first questions)

  1. Solve: 3x + 2y = 18 and x + 2y = 10
  2. Solve: 5x + 3y = 25 and 2x + 3y = 19
  3. Solve: 4x + y = 11 and 2x - y = 7
  4. Solve: x + 3y = 11 and 2x + y = 12

Quiz (sample)

  1. 1. Solve x + y = 7 and x - y = 3.

    • A. x=5, y=2
    • B. x=2, y=5
    • C. x=7, y=0
    • D. x=3, y=4

  2. 2. If you have 3x + 2y = 10 and 3x - y = 4, what is the best first step to eliminate x?

    • A. Add the equations
    • B. Subtract the equations
    • C. Multiply the equations
    • D. Divide the equations

  3. 3. If you add 5x + 7y = 20 and -5x + 5y = 10, what is the resulting equation?

    • A. 2y = 30
    • B. 12y = 30
    • C. 2y = 6
    • D. 12y = 6

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Support and Stretch worksheets, every answer and model answer, the teaching explainer and common misconceptions, editable and ready to print as PDF or Word.

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