Sistem persamaan Linear satu variabel. Cara menentukan himpunan penyelesaiannya

Introduction

This tutorial will guide you through solving linear equations with one variable. Understanding how to determine the solution set for these equations is essential in algebra and has real-world applications in various fields such as finance, engineering, and science.

Step 1: Understand the Structure of Linear Equations

• A linear equation in one variable can be expressed in the form:
  ax + b = 0
  where:
  • a is the coefficient of the variable x.
  • b is a constant.
  • x is the variable you want to solve for.

Practical Tip

• Ensure that a is not equal to zero, as this would not be a linear equation.

Step 2: Isolate the Variable

To find the value of x, you need to isolate it on one side of the equation. Follow these steps:

1. Subtract or add the constant: Move b to the other side of the equation by subtracting it from both sides.
   • Example: From ax + b = 0, you would write:
     ax = -b
2. Divide by the coefficient: Divide both sides by a to solve for x.
   • Example:
     x = -b/a

Common Pitfall

• Be careful with signs while moving terms across the equation. Always reverse the sign when you move a term to the other side.

Step 3: Check Your Solution

Once you have a proposed solution for x, substitute it back into the original equation to verify it works:

• If substituting x back into the equation makes both sides equal, then your solution is correct.

Real-World Application

• Solving linear equations is frequently used in budgeting. For example, if you know your total expenses and your income, you can set up a linear equation to find out how much you can spend on different categories.

Step 4: Write the Solution Set

The solution set for a linear equation in one variable is often a single value. However, if the equation is of the form 0 = 0, it has an infinite number of solutions, and you can express it as:

• x ∈ ℝ (x is any real number).

Practical Tip

• Always express your final answer clearly, indicating if it’s a specific number or a broader solution set.

Conclusion

In this tutorial, you learned how to solve linear equations in one variable by isolating the variable and verifying your solution. Mastering these steps is crucial for tackling more complex algebraic concepts. As a next step, practice by solving different linear equations to reinforce your understanding.