Cara Mudah Belajar Program Linear Bagian 1 - Matematika Wajib Kelas XI

Introduction

This tutorial provides a step-by-step guide to understanding linear programming, specifically focusing on the methods to determine the solution set of a system of linear inequalities with two variables. This is part of the compulsory mathematics curriculum for 11th-grade students. By following this guide, you will learn how to visualize solutions and formulate inequalities based on given conditions.

Step 1: Understanding Linear Inequalities

• Definition: Linear inequalities are mathematical expressions that represent a relationship between two variables, where one variable is either greater than, less than, greater than or equal to, or less than or equal to another.
• Standard Form: A linear inequality can be represented in the form:
  • Ax + By < C
  • Ax + By ≤ C
  • Ax + By > C
  • Ax + By ≥ C

Practical Advice

• Familiarize yourself with the terms used in inequalities (e.g., "less than" vs. "greater than").
• Ensure that you can identify and manipulate inequalities correctly.

Step 2: Finding the Solution Set

• Graphing Method:
  1. Convert each inequality into an equation (replace inequality sign with an equal sign).
  2. Graph the equations on a coordinate plane.
  3. Determine the boundary lines:
     • If the inequality is ≤ or ≥, use a solid line.
     • If the inequality is < or >, use a dashed line.
  4. Select a test point (usually (0,0) if it doesn’t lie on the line) to determine which side of the line to shade.

Practical Advice

• When shading the region, remember that the solution set is where the shaded areas overlap for all inequalities.
• Check multiple points if unsure about the shaded region.

Step 3: Formulating Linear Inequalities from a Solution Set

• Identifying Constraints:

  1. Observe the boundaries of the shaded region.
  2. Derive the linear inequalities that correspond to the edges of the shaded area.

• Example:

  • If the shaded area is bounded by the lines x + y = 5 and y = 2, the inequalities could be:
    • x + y ≤ 5
    • y ≥ 2

Practical Advice

• Take note of the intercepts where the lines cross the axes to help formulate the inequalities accurately.
• Ensure that the inequalities reflect the direction of the shaded region.

Conclusion

In this tutorial, you learned how to determine the solution set for a system of linear inequalities and how to formulate those inequalities based on a given solution area. Mastering these concepts is crucial for solving more complex problems in linear programming. For further practice, consider exploring additional resources or exercises related to linear inequalities and their applications in real-world scenarios. Happy studying!