Let the system of linear equations \(\begin{aligned}& x+y+k z=2 \\& 2 x+3 y-z=1 \\& 3 x+4 y+2 z=k\end{aligne…

Let the system of linear equations
\(\begin{aligned}& x+y+k z=2 \\& 2 x+3 y-z=1 \\& 3 x+4 y+2 z=k\end{aligned}\)
have infinitely many solutions. Then the system
\(\begin{aligned}& (k+1) x+(2 k-1) y=7 \\& (2 k+1) x+(k+5) y=10 \text { has: }\end{aligned}\)

[JEE Main 2023, 30 Jan (Shift 1)]