Use Cramer S Rule to Solve the System of Equations $\left\{ \begin{array} { l } x + 2 y + 2 z = 6 \\2 x + y + 2 z = 8 \\2 x + 2 y + z = - 4\end{array} \right.$

Essay

Use Cramer s rule to solve the system of equations, if possible. If the equations of the system are dependent, or if the system is inconsistent, so indicate. $\left\{ \begin{array} { l } x + 2 y + 2 z = 6 \\2 x + y + 2 z = 8 \\2 x + 2 y + z = - 4\end{array} \right.$