For the system of equations
$$
\begin{aligned}
& x+y+z=6 \\
& x+2 y+\alpha z=10
\end{aligned}
$$
$x+3 y+5 z=\beta$, which one of the following is NOT true?
(1) System has a unique solution for $\alpha=3, \beta \neq 14$.
(2) System has no solution for $\alpha=3, \beta=24$.
(3) System has a unique solution for $\alpha=-3, \beta=14$.
(4) System has infinitely many solutions for $\alpha=3, \beta=14$
Select the correct option:
A
System has a unique solution for $\alpha=3, \beta \neq 14$.
B
System has no solution for $\alpha=3, \beta=24$.
C
System has a unique solution for $\alpha=-3, \beta=14$.
D
System has infinitely many solutions for $\alpha=3, \beta=14$.
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