### Introduction

The need to solve systems of linear equations arises frequently in engineering. The analysis of electric circuits and the control of systems are two examples. Cramer’s rule for solving such systems involves the calculation of determinants and their ratio. For systems containing only a few equations it is a useful method of solution.

#### Prerequisites

- be able to evaluate $2\times 2$ and $3\times 3$ determinants

#### Learning Outcomes

- state and apply Cramer’s rule to find the solution of two simultaneous linear equations
- state and apply Cramer’s rule to find the solution of three simultaneous linear equations
- recognise cases where the solution is not unique or a solution does not exist

#### Contents

1 Solving two equations in two unknowns2 Solving three equations in three unknowns

3 Engineering Example 1

3.1 Stresses and strains on a section of material