This site uses cookie tracking technologies. Learn more in our Cookie Policy.
A factory produces three products P, Q and R. Each unit of each product requires time on Machine A, time on Machine B and a fixed quantity of raw material, as shown in the table below.
| Product | Machine A (hours) | Machine B (hours) | Raw material (kg) |
|---|---|---|---|
| P | 2 | 1 | 4 |
| Q | 3 | 2 | 1 |
| R | 5 | 4 | 2 |
On a particular day, the factory uses all of its available hours on Machine A, hours on Machine B and kg of raw material. Let , and denote the number of units of P, Q and R produced on that day.
Consider the system of linear equations
Consider the system of equations
Consider the system of equations
Factorise completely.
Practice IB Mathematics Analysis and Approaches (AA) Topic AHL 1.16—solution of Systems of Linear Equations with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for AHL 1.16—solution of Systems of Linear Equations and mirrors Paper 1, 2, 3 style where relevant.
Get instant solutions, detailed explanations, and build confidence with questions aligned to IB examiner expectations.
Each constraint can be interpreted as a plane in . Explain what your answer in part b) tells you about the geometric arrangement of these three planes.
where .
Write the system as an augmented matrix.
Use row reduction to reduce the augmented matrix to row-echelon form, in terms of .
where .
Solve the system.
State the geometric significance of your answer in terms of the three planes in .
