Solve the given system of equations. \[ \begin{array}{lr} 5 x+4 y-5 z= & -39 \\ 2 x-5 y+2 z= & 7 \\ 4 x-3 y+4 z= & 7 \end{array} \] Select the correct choice below and fill in any answer boxes within your choice. A. There is one solution. The solution set is $\{(-)$, (Simplify your answers.) B. There are infinitely many solutions. C. There is no solution.

Step 1 ：Given the system of equations: \[\begin{array}{lr} 5 x+4 y-5 z= & -39 \\ 2 x-5 y+2 z= & 7 \\ 4 x-3 y+4 z= & 7 \end{array}\]

Step 2 ：We can solve this system using the matrix method. The matrix method involves writing the system of equations in matrix form, then finding the inverse of the matrix if it exists and finally multiplying the inverse with the constants to get the solution.

Step 3 ：Write the system of equations in matrix form: \[A = \begin{bmatrix} 5 & 4 & -5 \\ 2 & -5 & 2 \\ 4 & -3 & 4 \end{bmatrix}, b = \begin{bmatrix} -39 \\ 7 \\ 7 \end{bmatrix}\]

Step 4 ：Find the inverse of matrix A and multiply it with matrix b to get the solution.

Step 5 ：The solution to the system of equations is \(x = -3\), \(y = -1\), and \(z = 4\).

Step 6 ：Final Answer: The solution set is \(\boxed{\{-3, -1, 4\}}\). Therefore, the correct choice is A.