Cramer's Rule is a method for solving systems of linear equations using determinants.

For a 2x2 system:

\(a_1x + b_1y = c_1\)

\(a_2x + b_2y = c_2\)

The solution is found by calculating three determinants:

\( D = \begin{vmatrix} a_1 & b_1 \\ a_2 & b_2 \end{vmatrix} \), \( D_x = \begin{vmatrix} c_1 & b_1 \\ c_2 & b_2 \end{vmatrix} \), \( D_y = \begin{vmatrix} a_1 & c_1 \\ a_2 & c_2 \end{vmatrix} \)

The variables are then \( x = \frac{D_x}{D} \) and \( y = \frac{D_y}{D} \).

A similar process applies to 3x3 systems. Note: Cramer's Rule only works if the main determinant \(D\) is not zero.