<P> In linear algebra , Cramer 's rule is an explicit formula for the solution of a system of linear equations with as many equations as unknowns , valid whenever the system has a unique solution . It expresses the solution in terms of the determinants of the ( square ) coefficient matrix and of matrices obtained from it by replacing one column by the vector of right - hand - sides of the equations . It is named after Gabriel Cramer ( 1704 -- 1752 ) , who published the rule for an arbitrary number of unknowns in 1750 , although Colin Maclaurin also published special cases of the rule in 1748 ( and possibly knew of it as early as 1729 ) . </P>
can cramer 's rule be used to solve any system of equations
Cramer 's rule is an explicit formula for the solution of a system of linear equations with as many equations as unknowns , valid whenever the system has a unique solution . It expresses the solution in terms of the determinants of the ( square ) coefficient matrix and of matrices obtained from it by replacing one column by the vector of right - hand - sides of the equations .