Solving Linear Equations

Equations and the Balance Method

Unknown on Both Sides

Equations and Fractions

Trial and Improvement

Solving Simultaneous Equations Graphically

Solving Simultaneous Equations using the Elimination Method

Problems with Simultaneous Equations

Solving Equations

Solving Equations with the Unknown on Both Sides

Solving Equations with Fractions

Simultaneous Equations by Elimination

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.