Matematika Kelas 9 Bab 1 SPLDV - Metode Grafik - hal. 17 - 20 - Kurikulum Merdeka

Introduction

This tutorial provides a step-by-step guide on solving systems of linear equations with two variables using the graphical method. It is based on the content from the video "Matematika Kelas 9 Bab 1 SPLDV - Metode Grafik" and aims to help students grasp the concepts effectively. Understanding this method is crucial for solving equations visually and interpreting their solutions.

Step 1: Understand the Basics of Linear Equations

• A linear equation in two variables can be expressed in the form: [ ax + by = c ] where:

  • (a), (b), and (c) are constants
  • (x) and (y) are variables

• Ensure you are familiar with key terms:

  • Variables: The unknowns we are trying to find.
  • Constants: The fixed numbers in the equation.

Step 2: Prepare the Equations

• Start with the system of equations you want to solve. For example:

  1. (2x + 3y = 6)
  2. (x - y = 1)

• Make sure both equations are in standard form (Ax + By = C).

Step 3: Find the Intercepts

• Calculate the x-intercept and y-intercept for each equation.

• For the first equation (2x + 3y = 6):

  • X-intercept: Set (y = 0) [ 2x + 3(0) = 6 \implies x = 3 ]
  • Y-intercept: Set (x = 0) [ 2(0) + 3y = 6 \implies y = 2 ]

• Repeat this for the second equation (x - y = 1):

  • X-intercept: Set (y = 0) [ x - 0 = 1 \implies x = 1 ]
  • Y-intercept: Set (x = 0) [ 0 - y = 1 \implies y = -1 ]

Step 4: Plot the Points on the Graph

• Draw a coordinate system (x-y plane).
• Plot the intercepts for both equations:
  • For the first equation, plot points (3, 0) and (0, 2).
  • For the second equation, plot points (1, 0) and (0, -1).

Step 5: Draw the Lines

• Connect the points for each equation with straight lines.
• Make sure to extend the lines across the graph for better visibility.

Step 6: Identify the Solution

• Look for the point where the two lines intersect. This point represents the solution to the system of equations.
• For the equations provided, the intersection might occur at a specific point, say (2, 0) depending on the lines drawn.

Common Pitfalls to Avoid

• Ensure the calculations for intercepts are correct.
• When plotting, be accurate with the scale to ensure the lines intersect precisely.
• Double-check that the lines are straight and extend across the graph.

Conclusion

In this tutorial, you learned how to solve systems of linear equations using the graphical method. You practiced finding intercepts, plotting points, and drawing lines to find the intersection, which represents the solution. As a next step, try solving different systems of equations using the same method to reinforce your understanding and skills.