2x2 Linear System Solver

Systems of linear equations arise in economic supply-and-demand equilibrium models, electrical Kirchhoff circuit loop analysis, and mixture problems in chemistry.

This solver takes the coefficients of two linear equations, computes the 2x2 determinant, and checks whether the system has a unique intersecting solution (x, y), is inconsistent (parallel lines with no solution), or dependent (infinitely many solutions).

Using Cramer's rule: determinant D = ad - bc. If D ≠ 0, x = (ed - bf) / D and y = (af - ec) / D. If D = 0, the lines are either parallel (inconsistent) or identical (coincident).