Level 2 Algebra Walkthrough
2025 NCEA Level 2 Algebra Question 2(e)
2025 Paper
Question
Here \(k\) is a non-zero constant.
Given that there is only one solution to the simultaneous equations, find the value of \(k\), then find the solution.
First walkthrough idea
Hint to try first
Start by making \(y\) the subject in the linear equation.
Step 1
Make y the subject
Adding \(2x\) to both sides gives \(y=2x+13\).
Show the first step’s working
Adding \(2x\) to both sides gives \(y=2x+13\).
Key result
Walkthrough overview
What this question practises
This 2025 walkthrough is part of AS91261 — Apply algebraic methods in solving problems.
Method: Using the discriminant in simultaneous equations.
This is Question 2(e) from the 2025 NCEA Level 2 Algebra paper for AS91261 — Apply algebraic methods in solving problems. Use the guided hints to practise the method before revealing the full working.
Calc.nz is an independent learning resource. Compare questions, diagrams, and assessment information with the official NZQA resources for AS91261.
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Learning summary
Review the method, not only the answer
This walkthrough helps you practise using the discriminant in simultaneous equations. Use the hints to plan the method, then repeat the question without hints and check each step.
Common mistake to avoid
Check each step against the original condition, preserve signs and restrictions, and confirm that the final result answers the question asked.