Solving Linear Equations

Students learn how to solve an equation using the balance method and trial and improvement.  As learning progresses they are taught how to form and solve a pair of simultaneous equations from known geometrical facts and real life problems.  This unit takes place in Year 9 Term 5 and leads on to solving and representing inequalities and inequations.


Solving Linear Equations Lessons

Revision Lessons

Prerequisite Knowledge
  • Use simple formulae
  • Generate and describe linear number sequences
  • Express missing number problems algebraically
  • Find pairs of numbers that satisfy an equation with two unknowns
  • Use and interpret algebraic notation
  • Simplify and manipulate algebraic expressions by:
    • collecting like terms
    • multiplying a single term over a bracket

Success Criteria
  • Solve linear equations in one unknown algebraically (including those with the unknown on both sides of the equation)
  • Solve two simultaneous equations in two variables algebraically;
  • Find approximate solutions to simultaneous equations in two variables using a graph;
  • solve linear equations in one unknown algebraically (including those with the unknown on both sides of the equation)
  • Translate simple situations or procedures into algebraic expressions or formulae; derive an equation (or two simultaneous equations), solve the equation(s) and interpret the solution.


Key Concepts
  • To solve an equation is to find the only value (or values) of the unknown that make the mathematical sentence correct.
  • For every unknown an equation is needed.
  • Students need to have a secure understanding of adding and subtracting with negatives when eliminating an unknown.
  • Coefficients need to be equal in magnitude to eliminate an unknown.

Common Misconceptions
  • Students can forget to apply the same operation to both sides of the equation therefore leaving it unbalanced.
  • Students often struggle knowing when to add or subtract the equations to eliminate the unknown. Review addition with negatives to address this.
  • Equations need to be aligned so that unknowns can be easily added or subtracted. If equations are not aligned students may add or subtract with non like variables.
  • Students often try to eliminate variables with their coefficients being equal.

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