Introduction

Solving Equations II – Edexcel GCSE (1MA1): Higher Tier

In this course, Professor Keith Ball (University of Warwick) continues his exploration of solving equations, covering Topics A19-A21 in the Pearson Edexcel GCSE (9-1) Mathematics (1MA1) Specification for Higher Tier. In the first mini-lecture, we give an introduction to solving simultaneous equations by looking at graphs and thinking about what it means for two equations to hold ‘simultaneously.’ In the second mini-lecture, we show how to solve simultaneous linear equations by substitution (Topic A19) before moving onto solving simultaneous linear equations by cancellation in mini-lecture three (Topic A19). In the fourth mini-lecture, we learn how to solve simultaneous linear and quadratic equations, that is, a pair of equations where one is linear and the other is quadratic (Topic A19). In the fifth mini-lecture, we learn how to find approximate solutions to equations using a technique called iteration (Topic A20). In the sixth and seventh mini-lectures, we look at how mathematical formulae appear in real-world applications and consider speed and distance, cost and rates, and Fahrenheit and Celsius, all of which involve linear or simultaneous equations (Topic A21).

Introduction

In this mini-lecture, we give an introduction to solving simultaneous equations by looking at graphs. In particular, we think about: (i) the equation and graph of a single straight line; (ii) the equations and graphs of two nonparallel straight lines, which must meet at one point; and (iii) how the point where two nonparallel straight lines meet satisfies both equations simultaneously.