System of equations (Cramer method)
Instant solution with detailed step-by-step output
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Calculator Systems of Equations
🔢 Solving systems of equations with step-by-step explanation
This tool finds the roots of linear equations for the systems 2×2 (two variables) and 3×3 (three variables). The main difference between our calculator is that it showsthe complete solutionand not just the final answer.
- Select the dimension of the system (2 or 3 equations).
- Enter coefficients for x, y, z and free terms.
- Obtain a solution using the Cramer method with the calculation of all determinants (Δ).
Where is this useful in practice?
Systems of equations are not just school algebra. Here are the real problems that this calculator solves:
- 📚 Study:Checking homework or test. You will see exactly where you made a mistake in calculating the determinant.
- ⚡ Physics (Electricity):Calculation of currents in electrical circuits using Kirchhoff's rules.
- 🧪 Chemistry: Equating complex chemical reactions (calculation of stoichiometric coefficients).
- 💼 Economics: Solving problems on mixtures and alloys. By the way, if you need to calculate the profit or discount as a percentage, use our percentage calculator.
Frequently asked questions (FAQ)
🔹 What method does the calculator use?
We use Cramer's method. It is ideal for learning, as it has a clear algorithm through the search for determinants of the matrix.
🔹 What to do if the main determinant is zero?
If the main determinant (Δ) is 0, then the system either has no solutions or has an infinite number of them. Cramer's method does not work in this case, and the calculator will report an error.
🔹 Is it possible to solve the 4x4 system?
The current version only supports systems with 2 and 3 unknowns, since they are most in demand in the school and university curriculum.