# Solving Linear Equations

Scheme of work: GCSE Higher: Year 9: Term 5: Solving Linear Equations

#### 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.

## Solving Linear Equations Resources

### Mr Mathematics Blog

#### 3D Vectors – Year 2

A-Level Scheme of work: Edexcel A-Level Mathematics Year 2: Pure 2: 3D Vectors

#### Parametric Equations

Edexcel A-Level Mathematics Year 2: Pure 2: Parametric Equations