Chapter 14: Simultaneous equations and iteration
The chapter problem: two taxi routes
Two taxi companies charge a fixed fee plus a price for each kilometre. A 4 km trip costs £14 with Company A and £16 with Company B. An 8 km trip costs £22 with Company A and £24 with Company B.
First contact: Which company do you predict charges more per kilometre? Estimate first. You can check your prediction at the end of the chapter.
By the end of this chapter you will be able to
- solve pairs of linear equations by elimination and substitution;
- find simultaneous solutions from graphs;
- solve a pair containing a linear and a quadratic equation;
- use iteration to find a numerical approximation.
Roadmap
- 14.1 Elimination
- 14.2 Substitution
- 14.3 Graphical solutions
- 14.4 Linear and quadratic equations — Higher only
- 14.5 Iteration — Higher only
- Review
Each section has a Learn page, Practise with help, and Practise. The Review page returns to the taxi fares and mixes methods from this chapter.
Your turn to connect it
Where might someone need to find two unknown amounts from two pieces of information? Write one example from your life, a job, or a subject you study. Say what the two unknowns would represent.