Consistency criterion using determinants for two variables for JEE

Formula

Unique solution if \(D\ne 0\); no solution if \(D=0\) and at least one of \(D_x,D_y\ne 0\); infinitely many solutions if \(D=D_x=D_y=0\).

Variables: \(D\): coefficient determinant, \(D_x,D_y\): Cramer determinants.

Conditions: For a 2\(\times\)2 linear system.

Determinant-based test of consistency.