Cramer's Rule

  The solution of the linear equations

is x = D₁/D, y = D₂/D, where D, D₁ and D₂ are determinants:

Cramer's rule is the general formula for n linear equations with n unknowns: each unknown x_i can be expressed as the quotient D_i/D where D is the determinant of the coefficient matrix, and D_i is D with the ith column replaced by the right-hand side. For large n, the method is both inefficient on computers and numerically unstable, and hence should in general not be used for numerical computations if n > 3.