Let \(\lambda, \mu \in R\). If the system of equations \( \begin{aligned} & 3 x+5 y+\lambda z=3 \\ & 7 x+11 y-9 …

Let \(\lambda, \mu \in R\). If the system of equations
\(
\begin{aligned}
& 3 x+5 y+\lambda z=3 \\
& 7 x+11 y-9 z=2 \\
& 97 x+155 y-189 z=\mu
\end{aligned}\)

has infinitely many solutions, then \(\mu+2 \lambda\) is equal to:

[JEE Main 2024, 9 Apr (Shift 1)]