Cramer's Rule is a mathematical theorem used to solve systems of linear equations with the same number of equations as unknowns. It provides a formula to find the values of the unknowns using determinants, which are special numbers calculated from the coefficients of the equations. This method is particularly useful for small systems, typically with two or three equations. To apply Cramer's Rule, you first calculate the determinant of the coefficient matrix. Then, for each variable, you replace the corresponding column of the matrix with the constants from the equations and calculate the determinant again. The value of each variable is found by dividing the determinant of the modified matrix by the determinant of the original matrix.