Math and Algebra
System of Equations Calculator
System of Equations Calculator solve a square system of up to six simultaneous linear equations with partial-pivot Gaussian elimination.
Math and Algebra
System of Equations Calculator
Solve a square system of up to six simultaneous linear equations with partial-pivot Gaussian elimination.
Formula
Solve A*x = b by row reduction with partial pivoting.
About the System of Equations Calculator
Solve a square system of up to six simultaneous linear equations with partial-pivot Gaussian elimination.
How the System of Equations Calculator Works
The coefficient matrix and constants are parsed, pivot rows are selected by magnitude, forward elimination creates an upper-triangular system, and back substitution produces each variable.
Formula
Solve A*x = b by row reduction with partial pivoting.
The calculation runs in your browser. Values are validated for required ranges, compatible units, and method-specific restrictions before results are displayed.
Required Inputs
- Coefficient matrix (required).
- Constants vector (required).
Results Reported
The result panel reports the final answer and the intermediate quantities needed to check the calculation:
- Equations
- Solution vector
- Maximum residual
System of Equations Calculator Example
Select Example Data in the calculator to load this reproducible input set:
| Input | Example value |
|---|---|
| Coefficient matrix | 1, 1
1, -1 |
| Constants vector | 5, 1 |
How to Use the Calculator
- Confirm that the calculator title and formula match the quantity you need.
- Enter every required value using the unit shown with its field.
- Select Example Data to inspect a valid input set, or enter your own values and select Calculate.
- Review all reported values and the displayed formula before using the answer.
- Use Copy Result or Download CSV when you need a reusable record.
Accuracy and Limitations
Enter one matrix row per line with the same number of coefficients as equations. Singular or nearly singular systems do not have one stable unique solution.
Keep units consistent, use measurements that represent the actual situation, retain full precision during the calculation, and round only the final answer. Professional decisions may require current official rules, field measurements, laboratory methods, or specialist review.
Frequently Asked Questions
What does the System of Equations Calculator calculate?
Solve a square system of up to six simultaneous linear equations with partial-pivot Gaussian elimination.
Which formula does the System of Equations Calculator use?
Solve A*x = b by row reduction with partial pivoting.
What should I verify before using this result?
Enter one matrix row per line with the same number of coefficients as equations. Singular or nearly singular systems do not have one stable unique solution.