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IB Maths AA HL Ahl 1 16 Hl Systems of Linear Equations Questions

Practise solving systems of up to three linear equations, classifying solution conditions, writing parametric solutions and verifying the result.

Syllabus
First assessment 2021
Course
Mathematics: analysis and approaches HL
Level
HL

Exam points

  • Solve a system of up to three linear equations by elimination, row reduction or an equivalent matrix method, showing the resulting values or relationships.
  • Use coefficient or parameter conditions to classify a system as having one solution, infinitely many solutions or no solution, and justify the classification.
  • Write a non-unique system’s general solution in parametric form with free variables clearly identified, then verify it in the original equations.

Learn this topic

Study AHL 1.16 (HL)—Systems of linear equations conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

IB Maths AA HL Ahl 1 16 Hl Systems of Linear Equations Questions question 1

[Maximum number: 5]

Find the values of k for which the following system of equations has no solutions and the value of k for the system to have an infinite number of solutions.

x−3y+z=3x+5y−2z=116y−6z=k\begin{aligned} & x-3 y+z=3 \\ & x+5 y-2 z=1 \\ & 16 y-6 z=k \end{aligned}
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