Cramer's rule expresses the solution to a system of simultaneous linear equaations in terms of ratios of determinants. It is widely known as an example of an impractical method for large systems because of the time required to compute the determinants. For 2-by-2 systems this time difficulty disappears and, since the method does not involve a search for pivots, it may appear to have an advantage over Gaussian elimination. In fact, methods based upon 2-by-2 Cramer's rule have been proposed for use on parallel computers. In this note we wish to point out that Cramer's rule is unsatisfactory even for 2-by-2 systems because of roundoff error difficulties.