Cramer's Rule Calculator
Solve systems of two or three linear equations using determinants. Enter the coefficients and constants to calculate each variable with Cramer's rule.
Enter the linear system
Solution
Cramer's rule formulas
Calculate det(A) from the coefficient matrix.
Replace one variable column with the constants to form Ax, Ay, or Az.
x = det(Ax)/det(A), y = det(Ay)/det(A), z = det(Az)/det(A).
Frequently asked questions
What is Cramer's rule?
Cramer's rule is a determinant-based method for solving a square system of linear equations. Each unknown is found by dividing a modified determinant by the determinant of the coefficient matrix.
When can Cramer's rule be used?
It can be used for a square system when the number of equations equals the number of variables and the coefficient determinant is nonzero.
What happens when det(A) equals zero?
The system does not have one unique solution, so division by det(A) is impossible. Another method such as Gaussian elimination is needed to determine whether the system is inconsistent or dependent.
Results are estimates generated locally in your browser using standard mathematical formulas. They are for informational and educational purposes only and are not a substitute for verification in coursework, examinations or professional contexts requiring certified accuracy. VisionVix accepts no liability for decisions based on this tool's output.
