Sistem Persamaan Linear Dua Variabel | SPLDV | Matematika Kelas 8 SMP/MTs

Introduction

This tutorial is designed to help you understand the concept of two-variable linear equations (SPLDV) as taught in the 8th-grade mathematics curriculum. It will guide you through various methods to solve these equations, including graphical representation, elimination, substitution, and a mixed approach. This foundational knowledge is essential for tackling more complex mathematical concepts in the future.

Step 1: Understanding Two-Variable Linear Equations

• A two-variable linear equation is typically written in the form:
  • ax + by = c
• Here, x and y are the variables, and a, b, and c are constants.
• The solution to these equations represents a point (x, y) on a coordinate plane.

Step 2: Graphical Method

• Plotting the Equations:
  1. Rewrite each equation in slope-intercept form (y = mx + b).
  2. Identify the slope (m) and the y-intercept (b).
  3. Plot the y-intercept on the graph.
  4. Use the slope to find another point.
  5. Draw the line through the points.
• Finding the Intersection:
  • The point where the two lines intersect represents the solution to the system of equations.

Practical Tip

• Ensure your graph is accurately scaled for better visualization of the intersection point.

Step 3: Elimination Method

• Steps to Solve:
  1. Align the equations vertically.
  2. Multiply one or both equations to match coefficients of one variable.
  3. Add or subtract the equations to eliminate one variable.
  4. Solve for the remaining variable.
  5. Substitute back to find the other variable.

Example

Given the equations:

1. 2x + 3y = 6
2. 4x - 3y = 12

Multiply the first equation by 2:

• 4x + 6y = 12

Now subtract the second equation:

• (4x + 6y) - (4x - 3y) = 12 - 12
• This simplifies to 9y = 0, so y = 0.

Substituting back to find x gives:

• 2x + 3(0) = 6 → x = 3.

Step 4: Substitution Method

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

Example

For the equations:

1. y = 2x + 1
2. x + y = 10

Substitute y in the second equation:

• x + (2x + 1) = 10 → 3x + 1 = 10 → 3x = 9 → x = 3.
• Then, substitute x back to find y: y = 2(3) + 1 = 7.

Step 5: Mixed Method

• This approach combines both elimination and substitution methods as needed.
• Use substitution when one equation is easily solvable for a variable, and elimination when coefficients align well.

Conclusion

In this tutorial, we covered the fundamental methods of solving two-variable linear equations (SPLDV). You learned about graphical representation, elimination, substitution, and mixed methods. Mastering these techniques will enable you to tackle complex systems of equations in future mathematical studies. For further practice, try solving different systems of equations using each method to solidify your understanding.