System of equations calculator
Solve linear systems of 2 or 3 equations with 2 or 3 unknowns, with determinants (Cramer's rule) and the classification of the system.
How to useSystem of linear equations
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System of equations calculator: what it is for
Type the coefficients of the equations and the calculator solves the system instantly, showing the values of x, y and z as fractions when possible. It also shows the main determinant and the determinant for each unknown.
When the determinant is zero, it classifies the system as inconsistent or dependent.
How to use
- Choose 2 or 3 equations.
- Type the coefficients and the results.
- See the solution and the determinants.
When to use it
- Solving high school math exercises.
- Checking work for tests and exams.
- Solving problems with two or three unknowns.
Frequently asked questions
How does the calculator solve the system?
With Cramer's rule: it calculates the main determinant and the determinant for each unknown. Each value is the unknown's determinant divided by the main one.
What do inconsistent and dependent systems mean?
When the main determinant is zero, the system has no unique solution: it is inconsistent (no solution, parallel lines) or dependent (infinitely many solutions, identical lines).
Is it really free?
Yes, 100% free. No sign-up, no subscription and no usage limits. All Tools123 tools are free and run right in your browser.