Solve the system. If there is no solution or if there are infinitely many solutions and the systern's equations are dependent, so state. \[ \begin{array}{rr} 6 x-y+3 z= & 9 \\ x+3 y-z= & -5 \\ 3 x+3 y-4 z= & 5 \end{array} \] Select the correct choice below and fill in any answer boxes within your choice. A. There is one solution. The solution set is $\{(\square, \square, \square)\}$. (Simplify your answers.) B. There are infinitely many solutions. c. There is no solution.

Step 1 ：Represent the system of equations in matrix form.

Step 2 ：Use Gaussian elimination to reduce the system to its row echelon form.

Step 3 ：If the system has a unique solution, the row echelon form will have a leading 1 in each row. If the system has no solution or infinite solutions, the row echelon form will have a row of zeros.

Step 4 ：The matrix representation of the system is: \[ A = \begin{bmatrix} 6 & -1 & 3 \\ 1 & 3 & -1 \\ 3 & 3 & -4 \end{bmatrix}, b = \begin{bmatrix} 9 \\ -5 \\ 5 \end{bmatrix} \]

Step 5 ：Solving the system gives the solution: \[ x = \begin{bmatrix} 2 \\ -3 \\ -2 \end{bmatrix} \]

Step 6 ：Therefore, the system has a unique solution and it is (2, -3, -2).

Step 7 ：Final Answer: \(\boxed{\{(2, -3, -2)\}}\)