System of Equations Solver

Solve systems of linear equations with 2 or 3 variables instantly using Cramer's Rule. Get step-by-step solutions showing determinant calculations for each variable.

1. Select 2 variables or 3 variables mode
2. Enter the coefficients for each equation
3. The solution calculates automatically as you type
4. View step-by-step determinant calculations

• 2×2 and 3×3 systems — Toggle between 2 and 3 variable systems
• Cramer's Rule — Solves using determinant method
• Special cases — Detects dependent and inconsistent systems
• Fraction results — Displays solutions as fractions when possible
• Step-by-step — Shows all determinant calculations

What is Cramer's Rule?

A method that uses determinants to solve systems of linear equations. Each variable equals the ratio of two determinants.

When does a system have no solution?

When the main determinant D = 0 and at least one of Dx, Dy (or Dz) is non-zero — the equations are contradictory.

When does it have infinite solutions?

When all determinants (D, Dx, Dy, Dz) equal 0 — the equations are dependent.