Solve the given system of equations.
$\begin{array}{l} 5 x + 4 y - 5 z = - 35 \\ 3 x - 5 y + 3 z = 10 \\ 6 x - 3 y + 6 z = - 15 \end{array}$
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

Finally, we can conclude that the solution to the system of equations is $(- 4, - 5, - 1)$ . Therefore, the correct choice is A. The solution set is ${(- 4, - 5, - 1)}$ .

Steps

Step 1 ：First, we represent the system of equations in matrix form. The matrix A is $[\begin{matrix} 5 & 4 & - 5 \\ 3 & - 5 & 3 \\ 6 & - 3 & 6 \end{matrix}]$ and the matrix B is $[\begin{matrix} - 35 \\ 10 \\ - 15 \end{matrix}]$ .

Step 2 ：We then solve the system of equations using the matrix method. The solution is $[\begin{matrix} - 4 \\ - 5 \\ - 1 \end{matrix}]$ .

Step 3 ：Finally, we can conclude that the solution to the system of equations is $(- 4, - 5, - 1)$ . Therefore, the correct choice is A. The solution set is ${(- 4, - 5, - 1)}$ .

Answer

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