PERTIDAKSAMAAN LINEAR DUA VARIABEL

Introduction

In this tutorial, we will explore how to determine the solution area for linear inequalities involving two variables. This topic is essential for understanding graphing inequalities in mathematics and has practical applications in various fields, such as economics and engineering. By the end of this guide, you will be able to graphically represent the solution areas of linear inequalities and interpret them effectively.

Step 1: Understand Linear Inequalities

Linear inequalities are expressions that relate a linear function to a value using inequality symbols such as <, >, ≤, or ≥. To work with these inequalities, you need to:

• Recognize the standard form of a linear inequality:
  • For example, ( ax + by < c )
• Understand the meaning of the inequality symbol:
  • < means "less than"

  • means "greater than"

  • ≤ means "less than or equal to"
  • ≥ means "greater than or equal to"

Step 2: Convert the Inequality into an Equation

To graph a linear inequality, first convert it into an equation:

• Change the inequality symbol to an equal sign.
• For example, if you have ( 2x + 3y < 6 ), convert it to ( 2x + 3y = 6 ).

Step 3: Graph the Boundary Line

Now, graph the boundary line derived from the equation:

1. Identify the intercepts:
   • Set ( x = 0 ) to find the y-intercept.
   • Set ( y = 0 ) to find the x-intercept.
2. Plot the points on a graph.
3. Draw the boundary line:
   • Use a solid line for ≤ or ≥.
   • Use a dashed line for < or >.

Step 4: Determine the Solution Area

To find the solution area for the inequality:

1. Choose a test point not on the boundary line (the origin (0,0) is often a good choice).
2. Substitute the test point into the original inequality:
   • If the inequality holds true, the area that includes the test point is part of the solution.
   • If it does not hold, the opposite area is the solution.
3. Shade the appropriate region on the graph to indicate the solution area.

Step 5: Check for Multiple Inequalities

When dealing with systems of linear inequalities:

1. Repeat Steps 1 to 4 for each inequality.
2. Identify the intersection of the shaded areas:
   • The common shaded region represents the solution set for the system of inequalities.

Conclusion

In this tutorial, we covered how to determine the solution area for linear inequalities involving two variables. You learned to convert inequalities into equations, graph boundary lines, and identify solution areas through shading. Understanding these concepts not only enhances your mathematical skills but also applies to real-world scenarios. Practice with different inequalities to solidify your understanding and explore further applications in your studies.