Simultaneous equations: substitution, lines and curves
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The teaching part (1 min) is free to watch. A free account opens the whole lecture: 1 worked example, 4 practice questions, 2 real past-paper questions with the answers explained, the mistakes that lose marks, the full-marks tip, a one-card summary and a quick quiz.
What this lecture covers
- Two unknowns, one trick
- Substitution for a hidden quadratic
Read the transcript of the teaching part
Last time
Before we start: last time, in Modulus equations and inequalities, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.
Two unknowns, one trick
Two equations, two unknowns. For two straight lines you add or subtract. But when one equation is a curve, that trick fails. The tool that always works is substitution: make one letter the subject of the easy equation, and put it into the hard one.
Substitution for a hidden quadratic
Some equations are quadratics in disguise. A power, a root or a bracket appears twice, once squared. Give the repeat a new letter, such as u. The equation becomes an ordinary quadratic in u. Solve for u, then go back and find x. Check every value of u is allowed.
How often it comes up
How often Cambridge has asked each part, counted by ExamYard from every past paper in its question bank: Equations solved by substitution.
The whole chapter: Equations, Inequalities and Graphs, Simultaneous Equations.
Chapter 5: Simultaneous equations
- Simultaneous equations: substitution, lines and curves 6 min
Also for O Level Additional Maths 4037
Which topics come up most in O Level Additional Maths 4037 past papers, counted from every paper since 2004.