\[
\left\{\begin{array}{l}
3 x+2 y-z=-5 \\
-x-y+z=1 \\
5 x+4 y-3 z=-7
\end{array}\right.
\]
hoose the best description of its solution. applicable, give its solution.
The system has no solution.
The system has a unique solution.
\[
(x, y, z)=(\square, \square, \square)
\]

The system has infinitely many solutions.
\[
(x, y, z)=
\]
$(x, \square, \square)$
$(\square, y, \square)$
(1]: )
Check:

Step 1 ：The system of equations is: \(3x + 2y - z = -5\), \(-x - y + z = 1\), and \(5x + 4y - 3z = -7\)

Step 2 ：Add the first and second equations to eliminate z: \((3x + 2y - z) + (-x - y + z) = -5 + 1\) which simplifies to \(2x + y = -4\)

Step 3 ：This gives us a new equation: \(2x + y = -4\)

Step 4 ：Multiply the second equation by 3 and add it to the third equation to eliminate z: \(3(-x - y + z) + (5x + 4y - 3z) = 3*1 + -7\) which simplifies to \(2x + y = -4\)

Step 5 ：This gives us the same equation again: \(2x + y = -4\)

Step 6 ：Since we have two identical equations, the system of equations is dependent and has infinitely many solutions.

Step 7 ：\(\boxed{\text{The solutions can be written in the form } (x, y, z) = (t, -2t-4, 3t+5) \text{ for any real number } t}\)