Let the system of equations \(x+5y-z=1\\ 4x+3y-3z=7\\ 24x+y+\lambda z=\mu\) \(\lambda ,\mu \in \mathrm{R}\), have infini…

Let the system of equations
\(x+5y-z=1\\ 4x+3y-3z=7\\ 24x+y+\lambda z=\mu\)

\(\lambda ,\mu \in \mathrm{R}\), have infinitely many solutions.

Then the number of the solutions of this system,If \(x,y,z\) are integers and satisfy \(7\leq x+y+z\leq 77\), is

[JEE Main 2025, 7 Apr (Shift 2)]