For the system of equations \[ \begin{aligned} & x+y+z=6 \\ & x+2 y+\alpha z=10 \end{aligned} \] \(x+3 y+5 z=\be…

\(
\text { System has a unique solution for } \alpha=3, \beta \neq 14 \text {. }
\)

\(
\text { System has no solution for } \alpha=3, \beta=4 \text {. }
\)

\(
\text { System has a unique solution for } \alpha=-3, \beta=14 \text {. }
\)

\(
\text { System has infinitely many solutions for } \alpha=3, \beta=14 \text {. }
\)