System of Linear Equations Solver
Solve systems of 2 or 3 linear equations using Cramer's rule. Get the determinant, variable values, and step-by-step solution for any system of linear equations.
Coefficients / Constants
a₁x + b₁y = c₁ , a₂x + b₂y = c₂
How to Use the System of Linear Equations Solver
- Enter the numbers or values in the input fields.
- The result is calculated and displayed automatically.
- Review the step-by-step solution or detailed breakdown.
- Copy the result or adjust inputs for a new calculation.
Referencia Rápida
| De | A |
|---|---|
| 2 + 3 | 5 |
| 12 × 12 | 144 |
| √144 | 12 |
| 2¹⁰ | 1,024 |
| π | 3.14159 |
| e | 2.71828 |
Casos de Uso
- •Checking homework or exam answers quickly and accurately.
- •Verifying manual calculations in professional or academic work.
- •Learning mathematical concepts with instant visual feedback.
- •Performing quick computations during meetings or presentations.
Fórmula
Cramer's rule solves a system of linear equations using determinants. For a 2×2 system: x = Dx/D, y = Dy/D, where D is the coefficient determinant, Dx replaces the x-column with constants, and Dy replaces the y-column. If D = 0, the system has no unique solution.
Preguntas Frecuentes
What is Cramer's rule?
Cramer's rule is a method for solving systems of linear equations using determinants. Each variable equals the ratio of a modified determinant (where one column is replaced by the constants) to the main coefficient determinant.
When does a system have no solution?
A system has no solution when the coefficient determinant D = 0 and at least one of the numerator determinants (Dx, Dy, Dz) is non-zero. This means the equations are contradictory.
When does a system have infinitely many solutions?
A system has infinitely many solutions when D = 0 and all numerator determinants are also zero. This means the equations are dependent — they describe the same line or plane.
Can I solve a 3×3 system with this calculator?
Yes. Switch to 3×3 mode to enter 9 coefficients and 3 constants. The calculator uses 3×3 determinants via Cramer's rule to find x, y, and z.