Pre-sessionals - Maths 3
Contact
- Name: Domenico Mergoni
- Email: d.mergoni -at- lse.ac.uk
- Work: London School of Economics
Tip
Internet is a great resource. Use it. Some resources I like:
Systems of Linear Equations
Introduction to Systems of Equations
- What is a System of Equations?
- Definition of a system of equations as a set of equations with common variables.
- Example: Discuss a system representing the total cost of items purchased.
- Methods for Solving Systems
- Briefly explain graphing, substitution, and elimination methods.
- Highlight when each method is most suitable.
- Exercise: Identify which method is best for a given system.
- Importance and Applications
- Emphasize the significance of systems of equations in solving real-world problems.
- Mention applications in various fields.
- Exercise: Brainstorm other scenarios where systems could be applied.
- What is a System of Equations?
Graphical Solution
- Solving Systems Graphically
- Explain the concept of solution points as intersections of graphs.
- Example: Solve the system \(2x + y = 5\) and \(3x -y = 1\) graphically.
- Exercise: Graph and solve simple systems of equations.
- Interpreting Solutions on Graphs
- Discuss the significance of unique solutions, no solutions, and infinite solutions.
- Interpret the graphical meaning of these cases.
- Exercise: Analyze different scenarios on graphs.
- Advantages and Limitations
- Compare graphical method with other methods.
- Discuss accuracy and limitations of graphical solutions.
- Solving Systems Graphically
Substitution and Elimination Methods
- Solving Systems using Substitution
- Explain the substitution method step by step.
- Example: Solve the system \(3x -2y = 8\) and \(x + y = 3\) using substitution.
- Exercise: Practice solving systems using the substitution method.
- Solving Systems using Elimination
- Explain the elimination (addition) method step by step.
- Example: Solve the system \(2x + 3y = 7\) and \(4x -y = 5\) using elimination.
- Exercise: Practice solving systems using the elimination method.
- Solving Systems using Substitution
Applications of Systems of Equations
- Real-World Examples of Systems
- Discuss examples from fields like economics, chemistry, and engineering.
- Example: Discuss a mixture problem involving two solutions.
- Exercise: Brainstorm more real-world examples.
- Using Systems to Solve Practical Problems
- Explain how to set up and solve practical problems using systems.
- Example: Solve a money-related problem involving different types of coins.
- Exercise: Solve practical problems related to mixtures, interest, or other scenarios.
- Reflection on Problem-Solving
- Highlight the problem-solving process and the role of systems.
- Encourage students to think critically and apply these methods.
- Real-World Examples of Systems
Conclusion and Recap
- Summarize the key concepts covered in the lecture.
Q&A Session