1. STROUD Worked examples and exercises are in the text 1 STROUD Worked examples and exercises are in the text Programme F5: Linear equations PROGRAMME F5 LINEAR EQUATIONS

2. STROUD Worked examples and exercises are in the text 2 STROUD Worked examples and exercises are in the text Programme F5: Linear equations Linear equations Simultaneous linear equations with two unknowns Simultaneous linear equations with three unknowns

3. STROUD Worked examples and exercises are in the text 3 STROUD Worked examples and exercises are in the text Programme F5: Linear equations Linear equations Simultaneous linear equations with two unknowns Simultaneous linear equations with three unknowns

4. STROUD Worked examples and exercises are in the text 4 STROUD Worked examples and exercises are in the text Programme F5: Linear equations Linear equations Solution of simple equations A linear equation in a single variable (unknown) involves powers of the variable no higher than the first. A linear equation is also referred to as a simple equation. The solution of simple equations consists essentially of simplifying the expressions on each side of the equation to obtain an equation of the form:

5. STROUD Worked examples and exercises are in the text 5 STROUD Worked examples and exercises are in the text Programme F5: Linear equations Linear equations Simultaneous linear equations with two unknowns Simultaneous linear equations with three unknowns

6. STROUD Worked examples and exercises are in the text 6 STROUD Worked examples and exercises are in the text Programme F5: Linear equations Linear equations Simultaneous linear equations with two unknowns Simultaneous linear equations with three unknowns

7. STROUD Worked examples and exercises are in the text 7 STROUD Worked examples and exercises are in the text Programme F5: Linear equations Simultaneous linear equations with two unknowns Solution by substitution Solution by equating coefficients

8. STROUD Worked examples and exercises are in the text 8 STROUD Worked examples and exercises are in the text Programme F5: Linear equations Simultaneous linear equations with two unknowns Solution by substitution A linear equation in two variables has an infinite number of solutions. For two such equations there may be just one pair of x- and y-values that satisfy both simultaneously. For example:

9. STROUD Worked examples and exercises are in the text 9 STROUD Worked examples and exercises are in the text Programme F5: Linear equations Simultaneous linear equations with two unknowns Solution by equating coefficients Example: Multiply (a) by 3 (the coefficient of y in (b)) and multiply (b) by 2 (the coefficient of y in (a))

10. STROUD Worked examples and exercises are in the text 10 STROUD Worked examples and exercises are in the text Programme F5: Linear equations Linear equations Simultaneous linear equations with two unknowns Simultaneous linear equations with three unknowns

11. STROUD Worked examples and exercises are in the text 11 STROUD Worked examples and exercises are in the text Programme F5: Linear equations Linear equations Simultaneous linear equations with two unknowns Simultaneous linear equations with three unknowns

12. STROUD Worked examples and exercises are in the text 12 STROUD Worked examples and exercises are in the text Programme F5: Linear equations Simultaneous linear equations with three unknowns With three unknowns and three equations the method of solution is just an extension of the work with two unknowns. By equating the coefficients of one of the variables it can be eliminated to give two equations in two unknowns. These can be solved in the usual manner and the value of the third variable evaluated by substitution.

13. STROUD Worked examples and exercises are in the text 13 STROUD Worked examples and exercises are in the text Programme F5: Linear equations Simultaneous linear equations Pre-simplification Sometimes, the given equations need to be simplified before the method of solution can be carried out. For example, to solve: Simplification yields:

14. STROUD Worked examples and exercises are in the text 14 STROUD Worked examples and exercises are in the text Programme F5: Linear equations Learning outcomes Solve any linear equation Solve simultaneous linear equations in two unknowns Solve simultaneous linear equations in three unknowns