Cramer's Rule Calculator
Solve a system of two linear equations using determinants.
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Request a ToolHow to Use the Cramer's Rule Calculator
This tool solves a 2x2 system of linear equations using Cramer's Rule.
- Enter the first equation. Provide coefficients a1, b1, and the constant c1.
- Enter the second equation. Provide coefficients a2, b2, and the constant c2.
- Read the solution. The values of x and y appear along with all three determinants (D, Dx, Dy).
About Cramer's Rule
Cramer's Rule uses determinants to solve a system of linear equations. For a 2x2 system, the main determinant D = a1*b2 - a2*b1. If D is not zero, the system has a unique solution: x = Dx/D and y = Dy/D, where Dx and Dy are determinants formed by replacing the appropriate column with the constants. When D equals zero the system has either no solution or infinitely many solutions.
Frequently Asked Questions
What happens when the determinant D is zero?
When D = 0, the system has no unique solution. The equations are either parallel (no solution) or identical (infinitely many solutions).
Does Cramer's Rule work for 3x3 systems?
Yes, Cramer's Rule extends to any n x n system. This calculator handles the 2x2 case. For larger systems, the number of determinants grows accordingly.
When should I use Cramer's Rule vs. elimination?
Cramer's Rule is efficient for small systems (2x2 or 3x3). For larger systems, Gaussian elimination or matrix methods are faster.