Cramer's rule

A system of linear equations with as many equations as unknowns can be solved explicitly using Cramer's rule whenever the system has a single solution. The answer is expressed in terms of the determinants of the (square) coefficient matrix and matrices created by substituting the column vector of the right-sides of the equations for one of its columns. Although Colin Maclaurin also presented specific examples of the rule in 1748, the rule is named after Gabriel Cramer (1704–1752), who published it in 1750.