Solving Linear Equations

August 23, 2016

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
Algebra: Interactive Lessons
Simultaneous Equations by Substitution
4 Part Lesson
Simultaneous Equations by Substitution
How to solve a pair of simultaneous equations using the substitution method.
Algebra: Interactive Lessons
Complex Linear Equations
4 Part Lesson
Complex Linear Equations
Students learn how to solve linear equations involving fractions
Algebra: Interactive Lessons
Solving Simultaneous Equations
4 Part Lesson
Solving Simultaneous Equations
Students learn how to solve a pair of simultaneous equation using the elimination method.
Algebra: Interactive Lessons
Problems with Simultaneous Equations
4 Part Lesson
Problems with Simultaneous Equations
Students learn how to set up and solve a pair of simultaneous equations.
Algebra: Interactive Lessons
Solving Simultaneous Equations Graphically
4 Part Lesson
Solving Simultaneous Equations Graphically
Students learn how to solve a pair of simultaneous equations graphically.
Algebra: Interactive Lessons
Equations with Fractions
4 Part Lesson
Equations with Fractions
Students learn how to use the balance method to solve equations involving fractions.
Algebra: Interactive Lessons
Equations with the Unknown on Both Sides
4 Part Lesson
Equations with the Unknown on Both Sides
Students learn how to solve equations where the unknown appears on both sides.
Algebra: Interactive Lessons
Solving Equations
4 Part Lesson
Solving Equations
Students learn how to solve one-step equations using the balance method.
Additional Resources
Algebra: Interactive Lessons
Two-Step Equations
Extended Learning
Two-Step Equations
Students gain additional practice solving two-step equations.
Algebra: Interactive Lessons
Equations with Unknown on Both Sides
Extended Learning
Equations with Unknown on Both Sides
Students gain additional practice solving a linear equation where the unknown appears on both sides.
Algebra: Interactive Lessons
Simultaneous Equations
Extended Learning
Simultaneous Equations
Students gain additional practice solving simultaneous equation through elimination.
Algebra: Free Resources
Problem Solving - Linear Equations
Problem Solving
Linear Equations
Five problem solving questions linking linear equations to area, capacity, averages and more.
Algebra: Interactive Lessons
Problem Solving with Simultaneous Equations
Problem Solving
Simultaneous Equations
Students are challenged to solve a range of problems involving simultaneous equations.
Algebra: Interactive Lessons
Revising Simultaneous Equations by Elimination
Revision
Simultaneous Equations by Elimination
Students revise how to solve a pair of simultaneous equation by elimination.
Algebra: Interactive Lessons
Revising Solving Equations
Revision
Solving Equations
Students revise how to use the balance method to solve two-step equations.
Algebra: Interactive Lessons
Revising Solving Equations with Fractions
Revision
Solving Equations with Fractions
Students revise how to solve equations involving fractions using the balance method.
Algebra: Interactive Lessons
Solving Equations with the Unknown on Both Sides
Revision
Equations with the Unknown on Both Sides
Revision lesson on solving equations with the unknown on both sides for exam students.
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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