Math Solvers/Algebra & Calculus/linear-equations-system

System of Linear Equations Solver (2×2 & 3×3)

Interactive simultaneous equation solver supporting both 2-variable and 3-variable linear systems with full determinant expansion and consistency checks.

Linear Equations (a₁x + b₁y = c₁)

Equation 1

Equation 2

Value of x

1.0000

Value of y

2.0000

Determinants:

D = -5.0000, Dx = -5.0000, Dy = -10.0000

Cramer's Rule Solution Steps

1. System Representation in Matrix Form

Linear system with coefficient matrix A and constant vector B.

2. Main Coefficient Determinant (D)

D ≠ 0 confirms a single unique solution exists.

3. Component Determinants (Dx and Dy)

Computed by replacing x and y coefficient columns with constants vector.

4. Cramer's Rule Solution

Unique intersection point (x, y) = (1.0000, 2.0000).

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Mathematical Formulation

Standard analytical and numerical formulations derived from classical algebra, linear algebra, and calculus principles.