Cara Mudah Menyelesaikan Sistem Pertidaksamaan Linear Dua VAriabel _ Dasar Program Linear

Introduction

This tutorial will guide you through the process of solving systems of linear inequalities in two variables, a fundamental concept in linear programming. By the end of this guide, you will know how to graph the solution area of these inequalities and identify feasible regions.

Step 1: Understanding the Inequalities

Before you can graph the solution area, you need to grasp the inequalities involved.

• Identify the inequalities: These will typically be in the form of:
  • Ax + By < C
  • Ax + By > C
  • Ax + By ≤ C
  • Ax + By ≥ C
• Recognize the significance of each inequality: The symbols (<, >, ≤, ≥) indicate whether the boundary line should be dashed or solid.
  • Use a solid line for ≤ or ≥.
  • Use a dashed line for < or >.

Step 2: Graphing the Boundary Lines

Once you understand the inequalities, the next step is to graph the boundary lines.

1. Convert inequalities to equations: Replace the inequality sign with an equal sign (e.g., Ax + By = C).
2. Find the intercepts:
   • X-intercept: Set y = 0 and solve for x.
   • Y-intercept: Set x = 0 and solve for y.
3. Plot the intercepts on a coordinate plane.
4. Draw the line connecting the intercepts, ensuring to use the correct line type (solid or dashed).

Step 3: Testing Points to Identify the Solution Area

To determine which side of the line is part of the solution, you must test a point.

1. Choose a test point: (0,0) is often a convenient choice unless it lies on the boundary line.
2. Substitute the point into the original inequality:
   • If the inequality holds true, the region containing the test point is part of the solution area.
   • If false, the opposite side of the line is the solution area.
3. Shade the appropriate region: Use a pencil or a highlighter to indicate the area that satisfies the inequality.

Step 4: Repeat for Each Inequality

You may have multiple inequalities in your system. Repeat the previous steps for each one:

• Graph each boundary line.
• Test points to determine the correct shading for each inequality.

Step 5: Finding the Feasible Region

After graphing all inequalities and their respective shaded areas, the final step is to identify the feasible region.

• Look for overlapping shaded areas: This region is where all conditions are satisfied.
• Outline this area clearly: This is your solution set for the system of inequalities.

Conclusion

You have now learned how to graph the solution area for systems of linear inequalities in two variables. By following these steps, you can visualize and solve linear programming problems effectively. For further practice, try working on different sets of inequalities to reinforce your understanding. Happy graphing!