Elimination Method Calculator
ax + by = c
dx + ey = f
dx + ey = f
First Equation
Second Equation
Solution Steps
How to Use
- Enter the coefficients a, b, c for the first equation
- Enter the coefficients d, e, f for the second equation
- Click "Solve by Elimination" to see the step-by-step solution
- View the final solution for x and y
About the Elimination Method
The elimination method is used to solve systems of linear equations by:
- Multiplying one or both equations by constants to make coefficients of one variable equal
- Adding or subtracting the equations to eliminate one variable
- Solving for the remaining variable
- Substituting back to find the other variable
The system must be consistent and independent for a unique solution.
Common Examples
| System | Solution |
|---|---|
|
2x + y = 5 x - y = 1 |
x = 2, y = 1 |
|
3x + 2y = 8 2x - y = 3 |
x = 2, y = 1 |
|
x + y = 4 x - y = 2 |
x = 3, y = 1 |
Applications
- Solving real-world problems with two variables
- Economics and business analysis
- Physics and engineering calculations
- Mathematical modeling
- Optimization problems
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