Sistem Pertidaksamaan Dua Variabel / SPtDV • Part 1: Pertidaksamaan Linear dan Kuadrat Dua Variabel

Introduction

This tutorial covers the basics of two-variable inequalities, focusing specifically on linear and quadratic inequalities. Understanding these concepts is essential for solving various mathematical problems and will set the foundation for more advanced topics in systems of inequalities.

Step 1: Understanding Two-Variable Inequalities

• Definition: A two-variable inequality is an inequality that involves two variables, commonly expressed in the form of:
  • Linear: ax + by > c
  • Quadratic: ax² + by² + cxy > d
• Purpose: These inequalities are used to describe regions on a graph where certain conditions hold true.

Step 2: Graphing the Solution Area

• Graph the Boundary:
  • For linear inequalities, first graph the corresponding equation as if it were an equality (replace the inequality with an equal sign).
  • Use a solid line for ≤ or ≥ and a dashed line for < or >.
• Determine the Shaded Area:
  • Choose a test point (commonly (0,0)) to determine which side of the boundary line to shade.
    • If the test point satisfies the inequality, shade the region containing that point.
    • If not, shade the opposite side.

Step 3: Graphing Functions

• Plotting Points:
  • Identify key points on the graph by substituting values of x to find corresponding y values.
• Drawing the Graph:
  • Connect the points using a smooth curve for quadratic functions or straight lines for linear functions.
• Labeling the Axes: Clearly label the x-axis and y-axis to avoid confusion.

Practical Tips

• Common Pitfalls:
  • Forgetting to use a dashed line for strict inequalities.
  • Misinterpreting the shaded area.
• Real-World Applications: Two-variable inequalities can be used in economics for cost and revenue analysis, in engineering for materials' strength calculations, and in planning for resource allocation.

Conclusion

Understanding two-variable inequalities is crucial for solving systems and visualizing solutions graphically. Practice by solving different inequalities and graphing them to strengthen your comprehension. For further learning, explore the next videos in the series that delve deeper into examples and applications of these concepts.