Sistem Persamaan Linier Dua Variabel (SPLDV) Metode Campuran (Eliminasi-Substitusi)

Introduction

This tutorial will guide you through solving a system of linear equations with two variables (SPLDV) using the mixed method of elimination and substitution. This approach is valuable for students and anyone looking to understand how to find solutions to these equations effectively.

Step 1: Understanding the System of Linear Equations

• A system of linear equations consists of two or more equations with the same set of variables.
• For two variables, the general form is:
  • Equation 1: ax + by = c
  • Equation 2: dx + ey = f
• The goal is to find the values of x and y that satisfy both equations simultaneously.

Step 2: Solving by Elimination Method

• Start with the two equations you have.
• Aim to eliminate one variable by manipulating the equations.
• Follow these sub-steps:
  1. Align the equations vertically.
  2. Multiply one or both equations to create coefficients that will cancel out one variable when added or subtracted.
  3. Add or subtract the equations to eliminate one variable.
  4. Solve for the remaining variable.

Example:

• Given equations:
  • 2x + 3y = 6 (Equation 1)
  • 4x - 3y = 12 (Equation 2)
• Multiply Equation 1 by 1 and Equation 2 by 1 (no change needed):
  • 2x + 3y = 6
  • 4x - 3y = 12
• Add the equations:
  • (2x + 4x) + (3y - 3y) = 6 + 12
  • 6x = 18
  • x = 3

Step 3: Substituting to Find the Other Variable

• Once you have the value of one variable, substitute it back into one of the original equations to solve for the other variable.
• For example:
  • Substitute x = 3 into Equation 1:
    • 2(3) + 3y = 6
    • 6 + 3y = 6
    • 3y = 0
    • y = 0

Step 4: Checking the Solution

• Always substitute both x and y back into the original equations to verify that they satisfy both.
• Using the values x = 3 and y = 0:
  • Equation 1: 2(3) + 3(0) = 6 (True)
  • Equation 2: 4(3) - 3(0) = 12 (True)

Step 5: Graphical Representation (Optional)

• For a better understanding, you can graph both equations on a coordinate plane.
• The point where the two lines intersect represents the solution to the system.

Conclusion

You have learned how to solve a system of linear equations with two variables using the elimination and substitution method. Remember to always check your solutions for accuracy. Practicing various problems will enhance your skills and understanding of SPLDV. For further study, consider exploring more complex systems or different methods of solving linear equations.