Linear Equation System Solver
Solve systems of linear equations in 2x2 or 3x3 form. This calculator uses determinant-based methods to return x, y, and z with clear results.
Loading calculator...
Related calculators
Back to Mathematical CalculationsAverage Calculator
Compute common averages from a list of values and compare their behavior.
Arithmetic
Perform basic arithmetic operations (addition, subtraction, multiplication, division) instantly with our free and simple online calculator.
Exponent Calculation
Instantly calculate the power of a number or its logarithm (finding the exponent). A free and practical tool for exponential and logarithmic operations.
Fraction Calculator
Calculate fraction operations with simplified and mixed-number results.
GCD & LCM
Calculate GCD and LCM for multiple integers with step-aware results and clear explanations.
Solving linear systems
A linear system can be written in matrix form as A * x = b, where A contains the coefficients and b contains the constants.
If the determinant of A is nonzero, the system has a unique solution. This calculator uses Cramer's rule to compute each variable.
When the determinant is zero, the system may have infinitely many solutions or no solution. In that case the solver reports that no unique solution exists.
Use the 2x2 mode for two-variable systems and the 3x3 mode for three-variable systems.