If $$A=\left( \begin{array}{ccc} a_{11} & a_{12} & a_{13} \\a_{21} & a_{22} & a_{23}\\ a_{31} & a_{32} & a_{33}\end{array} \right),$$

$$C=\left( \begin{array}{ccc} c_{1} \\ c_{2} \\c_{3} \end{array} \right),$$

Cramer's Rule : ${x_1}=\frac{\Delta_1}{\Delta_0}$ ,  ${x_2}=\frac{\Delta_2}{\Delta_0}$ , ${x_3}=\frac{\Delta_3}{\Delta_0}$

Where: $$\Delta_0=\left| \begin{array}{ccc} a_{11} & a_{12} & a_{13} \\a_{21} & a_{22} & a_{23}\\ a_{31} & a_{32} & a_{33}\end{array} \right|$$

$$\Delta_1=\left| \begin{array}{ccc} c_{1} & a_{12} & a_{13} \\c_{2} & a_{22} & a_{23}\\ c_{3} & a_{32} & a_{33}\end{array} \right|$$

$$\Delta_2=\left| \begin{array}{ccc} a_{11} & c_{1} & a_{13} \\a_{21} & c_{2} & a_{23}\\ a_{31} & c_{3} & a_{33}\end{array} \right|$$

$$\Delta_3=\left| \begin{array}{ccc} a_{11} & a_{12} & c_{1} \\a_{21} & a_{22} & c_{2}\\ a_{31} & a_{32} & c_{3}\end{array} \right|$$