Exam-style question
Try this first
Why is substitution often useful when one simultaneous equation is linear and the other is quadratic?.
- A.B4: justify each step using the relevant algebra and functions rule
- B.Use any familiar GCSE calculation even if it ignores solving simultaneous equations in two variables by elimination…
- C.Write only the final answer without showing the mathematical method
- D.Change the notation or restrictions to make the algebra look simpler
Model answer
What a good answer should say
- The correct answer is B4: justify each step using the relevant algebra and functions rule.
- Substitution is useful because the linear equation can express one variable in terms of the other, producing a quadratic equation whose roots give possible intersections.
This answer is tied to the objective: B4 Solve simultaneous equations in two variables by elimination and by substitution, including one linear and one quadratic equation..
Explanation
Why this works
Use the explanation to connect the worked answer back to B4 Solve simultaneous equations in two variables by elimination and by substitution, including one linear and one quadratic equation..
The correct option, B4: justify each step using the relevant algebra and functions rule, is supported because substitution turns the linear-quadratic pair into a single-variable quadratic. The intersection is a solution because it is the same point on both original graphs with equal y-values, so both coordinates must be checked for each root.
Maths method check
- Topic focus: Pure Mathematics.
- Question style: practice.
- Reasoning demand: understanding.
- Check the operation, notation, units, and final answer form against the question before moving on.
Common mistake
No common mistake is linked to this question yet.