Topic explanation
Solving simultaneous equations in two variables, both linear and linear/quadratic.
Key formulas & rules
- Elimination: align coefficients, add/subtract equations to eliminate one variable
- Substitution: y = … from one equation into the other
- For linear + quadratic: substitute, expand, rearrange to quadratic = 0, solve, then back-substitute
Common mistakes
- Forgetting to find **both** y-values when the quadratic gives two x-values (two intersection points).
- Adding equations when signs need subtracting (or vice versa) — track coefficients carefully.
- Giving solutions from only one equation — always check in the **other** equation.
Exam tips
- State the method (“substitute equation (1) into (2)…”) — it helps examiners award M marks.
- If answers look messy, check arithmetic on the quadratic before rejecting a root.
- Context questions: discard pairs that don’t make sense (negative length, etc.) only if the problem demands it.
Practice questions
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