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 ${(◻, ◻, ◻)}$ . (Simplify your answers.)
B. There are infinitely many solutions.
c. There is no solution.

Answer

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Answer

Final Answer: ${(2, - 3, - 2)}$

Steps

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: $A = [\begin{matrix} 6 & - 1 & 3 \\ 1 & 3 & - 1 \\ 3 & 3 & - 4 \end{matrix}], b = [\begin{matrix} 9 \\ - 5 \\ 5 \end{matrix}]$

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

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

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

Answer

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