Pre-sessionals - Maths 3

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.

• 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.

• 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.

• 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.

• Conclusion and Recap

  • Summarize the key concepts covered in the lecture.

• Q&A Session

• Exercises

• References