Systems of linear equations
Systems of linear equations for IB Analysis and Approaches HL: Gaussian elimination, classifying systems, systems with a parameter and IB exam questions.
A system of linear equations is a set of equations that must all hold at the same time. At Higher Level (HL) you work with three equations and three unknowns, and there may be a single solution, infinitely many or none. You will learn to tell them apart and to solve them with Gaussian elimination, and to discuss a system when a parameter appears. In Paper 2 the GDC solves systems with a unique solution, but the exam asks you to justify the special cases, so it is worth mastering the method by hand.
Recommended order
Start with what a system is and how it is classified, continue with Gaussian elimination to solve systems and recognise each case, and finish with systems with a parameter, which carry the most marks. At the end you have the IB exam questions grouped by type.
Linear equations and polynomials (topic 1).
Sections in this topic
Linear equations and systems
Linear equation in three unknowns, 3×3 system and its classification: unique solution, infinitely many or no solution. IB Analysis and Approaches HL.
3 worked examples Section 2Gaussian elimination method
Solve and classify 3×3 systems with Gaussian elimination: row operations, echelon form and back substitution. IB Analysis and Approaches HL.
3 worked examples Section 3Systems with a parameter
How to discuss a 3×3 system with a parameter: cases with one solution, infinitely many or none, conditions on constant terms and homogeneous systems. IB HL.
3 worked examples End of topicIB exam questions: topic 7
IB exam questions on systems of linear equations: solving 3×3 systems, discussion with a parameter and consistency conditions, with step-by-step solutions.
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