Unit 1: Number and Algebra
Topic 1.16: Systems of equations (HL only) Questions
Practice 20 exam-style questions for IB Math AA SL Topic 1.16. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
11 mark
2026
To eliminate x from x + 2y = 5 and 3x − y = 1, you could:
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Unlock Question2Write down2 marks
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Write down the solution of the system.
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2026
Adding x − y + z = 5 and x + y − z = 1 gives:
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2026
Determine the number of solutions: x + y + z = 1, x + y + z = 2, x − y + z = 0.
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2026
Elimination ends with 0 = 0. The system has:
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Write down the number of solutions the system has.
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2026
Three planes that are all parallel (and distinct) give:
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Best Paper-1 check that (1, 2, 3) solves a 3-equation system:
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2026
A linear system can have how many solutions?
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Determine the number of solutions: x + 2y − z = 3, 2x + 4y − 2z = 7, x − y + z = 0.
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Solve: x + y + z = 6, 2x + y + 3z = 14, x + 2y + z = 8.
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Solve: x + y = 5, y + z = 7, x + z = 6.
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Determine the number of solutions: x + y + z = 4, 2x + 2y + 2z = 8, x − y + z = 2.
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2026
A 3×3 system reduces to 2x + z = 5 and 2x + z = 5 (the same equation twice). This signals:
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Unlock Question16Explain2 marks
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Explain geometrically what 'no solution' means for three planes.
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2026
If one equation is a non-matching multiple of another (e.g. 2×LHS but wrong RHS), the system:
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2026
Two of three planes are identical and the third cuts them. The system has:
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2026
Solve: 3x + 2y + z = 10, x + y + z = 6, 2x + y − z = 1.
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2026
Find the value of for which the system does not have a unique solution, and state the nature of the solution set then.
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