System of Two Linear Equations
Solve a1*x + b1*y = c1; a2*x + b2*y = c2 via Cramer's rule. Reports unique / infinite / no-solution; shows the determinant.
Formula and source
det = a1*b2 - a2*b1. If det != 0: x = (c1*b2 - c2*b1)/det, y = (a1*c2 - a2*c1)/det (Cramer's rule). If det = 0 and (a1*c2 = a2*c1) and (b1*c2 = b2*c1): infinitely many solutions (same line). If det = 0 otherwise: no solution (parallel lines).
Standard linear algebra; Cramer's rule per Gabriel Cramer, 'Introduction a l'analyse des lignes courbes algebriques,' 1750.
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