First you transform the system to standard form like this

The determinant of the coefficient matrix of this system is

Since this is the system has a unique solution. To get the solution you plug in the right-hand side of the system into the corresponding column of the coefficient matrix and divide by the determinant of the coefficient matrix. For example to get the uniquely determined value of X, you replace the coefficients of X in the coefficient matrix with the right-hand side of the above system, like this

Similarly for Y and Z.