Answer
Compute $D,D_x,D_y,D_z$, then decide the nature of the system and find its solution (if it exists)
Work Step by Step
In order to apply Cramer's rule, we first compute the determinant $D$ of the system's coefficients.
The next step is to compute $D_x,D_y,D_z$ which are determinants built from determinant $D$ in which we replace the $x$, $y$ and $z$ column by the constant matrix.
If $D\not=0$, then the system has one solution:
$x=\dfrac{D_x}{D}$
$y=\dfrac{D_y}{D}$
$z=\dfrac{D_z}{D}$
If $D=0$ and $D_x=0$, D_y=0$, D_z=0$, the system is dependent (it has infinitely many solutions).
If $D=0$, but at least one of the determinants $D_x,D_y,D_z$ is not zero, then the system is inconsistent (it has no solution).
