Konsep Dasar Sistem Persamaan Linear Dua Variabel (SPLDV) | Matematika Wajib Kelas 10

Introduction

This tutorial provides a foundational understanding of the System of Linear Equations in Two Variables (SPLDV), a key concept in mathematics for 10th-grade students. By breaking down the essential components, you'll learn how to solve these equations and apply them in various contexts.

Step 1: Understanding Linear Equations

• Definition: A linear equation is an equation where the highest power of the variable is one. In two variables (x and y), it takes the form:
  • ax + by = c
• Components:
  • a and b are coefficients.
  • c is a constant.
• Graphical Representation: Linear equations can be represented graphically as straight lines on a coordinate plane.

Step 2: Introduction to Systems of Linear Equations

• Definition: A system of linear equations consists of two or more linear equations with the same variables.
• Example:
  • Equation 1: 2x + 3y = 6
  • Equation 2: x - y = 2
• Goal: The aim is to find the values of x and y that satisfy both equations simultaneously.

Step 3: Methods to Solve Systems of Linear Equations

• Substitution Method:

  1. Solve one equation for one variable.
  2. Substitute this expression into the other equation.
  3. Solve for the remaining variable.
  4. Substitute back to find the first variable.

• Elimination Method:

  1. Align the equations.
  2. Multiply one or both equations to make the coefficients of one variable the same.
  3. Subtract or add the equations to eliminate one variable.
  4. Solve for the remaining variable.
  5. Substitute back to find the other variable.

Step 4: Example Problem Solving

• Example System:
  • 2x + 3y = 6
  • x - y = 2
• Using the Elimination Method:
  1. Rearrange the second equation: x = y + 2.
  2. Substitute into the first equation:
     • 2(y + 2) + 3y = 6
     • 2y + 4 + 3y = 6
     • 5y + 4 = 6
     • 5y = 2 → y = 2/5
  3. Substitute y back into x = y + 2:
     • x = 2/5 + 2 = 12/5

Step 5: Graphical Solution

• Graphing the Equations:
  1. Convert each equation into slope-intercept form (y = mx + b).
  2. Plot both lines on a coordinate plane.
  3. Identify the intersection point, which represents the solution to the system.

Conclusion

In this tutorial, you learned about linear equations and how to work with systems of linear equations in two variables. You explored methods like substitution and elimination, practiced problem-solving with examples, and understood graphical representation. To deepen your understanding, practice with additional problems and explore real-world applications of linear equations, such as in finance or physics.