Introduction to Solving Simultaneous Equations

Solving Equations II – AQA GCSE (8300): Higher Tier

In this course, Professor Keith Ball (University of Warwick) continues his exploration of solving equations, covering Topics A19-A21 in the AQA GCSE (9-1) Mathematics (8300) 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 to Solving Simultaneous Equations

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.