There are plenty of direct and iterative methods to solve a linear algebraic system of equations. Using Cramer's rule, one can easily obtain the solution for small systems by hand. However, with the growth of the unknowns, the method becomes computationally very expensive. Moreover, calculating a determinant by its definition may result in overflow or underflow if someone wanted to apply it on a computer. That is why Cramer's algorithm is not applied in computations.