determinant

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Because the Vedic sutra does not rely on matrix determinants and because the calculation of the determinant of a 4 x 4 matrix could (if there are no zero elements) mean calculating 16 determinants of 3 x 3 matrices (with four unknowns this process would be repeated five times, for a total of eighty 3 x 3 determinants calculated which is roughly 480 calculations by the diagonal multiplication method which is one of the quicker ways to calculate the determinant of a 3 x 3 matrix) it stands to reason that with four equations and four unknowns, the Vedic technique could be superior to Cramer's rule.
In the case of four or more unknowns, where computing matrix determinants becomes inefficient, the question (for the moment unanswered) is whether row-reduction techniques are superior or not in terms of efficiency.