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Mathematics

Linear equation system solver

Solve two or three equations together. The calculator distinguishes a unique solution, contradictions and free variables.

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01

Your inputs

The starting values are an example.

For two equations, enter a; b; right-hand side on each line. For three equations: a; b; c; right-hand side. Put each equation on a separate line.

Decimals: 12.5 · Thousands: 1,234.56. Follow the field instructions for lists.

02

Your result

Enter your values and select Calculate.

Your calculation will appear here.

Your result will include the relevant values and units.

Understand the calculation

Formula and example

How it is calculated

A·x=b. Gauss–Jordan elimination transforms the augmented coefficient matrix using valid row operations.

Worked example

x+y=5 and x−y=1 give x=3 and y=2. Enter “1; 1; 5” and “1; −1; 1” on separate lines.

Things to check

  • The implementation uses floating-point numbers, row scaling and pivot selection. It is not a symbolic fraction solver.
  • Nearly dependent equations are numerically sensitive. For unique solutions, the substitution residual shows the largest remaining discrepancy.

Frequently asked questions

What does infinitely many solutions mean?

At least one variable remains free because the equations do not provide enough independent conditions. This differs from a contradictory system with no solution.