While Cramer's rule is certainly an elegant expression of the solution, it is not necessarily a useful way to solve a system of linear equations by hand where the number of equations is greater than about 3. This is because pencil-and-paper evaluation of determinants is a tedious and error-prone process. Computer programs to solve linear systems could use Cramer's rule, but they typically use ''Gaussian elimination'', which is the computer equivalent of the "multiply by a constant and subtract" method that is taught in algebra classes. | While Cramer's rule is certainly an elegant expression of the solution, it is not necessarily a useful way to solve a system of linear equations by hand where the number of equations is greater than about 3. This is because pencil-and-paper evaluation of determinants is a tedious and error-prone process. Computer programs to solve linear systems could use Cramer's rule, but they typically use ''Gaussian elimination'', which is the computer equivalent of the "multiply by a constant and subtract" method that is taught in algebra classes. |