Cara Menentukan Sistem Pertidaksamaan dari Grafik Daerah Penyelesaian

Introduction

In this tutorial, we will explore how to determine systems of inequalities from the graphical representation of solution areas. This method is crucial for visualizing and solving linear inequalities, particularly in two-variable systems. By the end of this guide, you'll be equipped with the techniques to interpret graphical data and derive the corresponding inequalities.

Step 1: Understand the Graphical Representation

• Start by analyzing the graph provided.
• Identify the shaded area, which represents the solution set for the inequalities.
• Recognize that the boundary lines (solid or dashed) indicate whether the points on the line are included in the solution:
  • Solid Line: Indicates that points on the line are part of the solution (≥ or ≤).
  • Dashed Line: Indicates that points on the line are not included (> or <).

Step 2: Identify the Boundary Lines

• Determine the equations of the boundary lines from the graph:
  • Look for intercepts and slopes.
  • Use the slope-intercept form (y = mx + b) to derive the equations.
• Example:
  • If the line crosses the y-axis at 2 and has a slope of -1, the equation is:

    y = -x + 2
    

Step 3: Determine the Inequalities

• Analyze the direction of the shading:
  • If the shaded area is above the line, use:
    • y > mx + b (for dashed lines)
    • y ≥ mx + b (for solid lines)
  • If the shaded area is below the line, use:
    • y < mx + b (for dashed lines)
    • y ≤ mx + b (for solid lines)
• Combine the inequalities from all boundary lines to create a system.

Step 4: Write the System of Inequalities

• Compile the inequalities you have determined into a formal system.
• Ensure that each inequality corresponds to its respective boundary condition and shading.

Step 5: Check the Solution Area

• Verify your inequalities by choosing a test point within the shaded region:
  • Substitute the test point into each inequality to check if they hold true.
• If all inequalities are satisfied, your system is correct.

Conclusion

In this tutorial, we've outlined the steps to determine systems of inequalities from graphical representations. By analyzing boundary lines, identifying shading directions, and formulating the corresponding inequalities, you can effectively interpret and solve problems involving linear inequalities. For further practice, try applying these steps to different graphs to solidify your understanding.