For the system of equations $x+y+z=6$ $x+2 y+\alpha z=10$ $x+3 y+5 z=\beta$, which one of the following is NOT true?

Question

For the system of equations

$x+y+z=6$

$x+2 y+\alpha z=10$

$x+3 y+5 z=\beta$, which one of the following is NOT true?

System has a unique solution for $\alpha=3,\beta\ne14$.

System has infinitely many solutions for $\alpha=3, \beta=14$.

System has no solution for $\alpha=3, \beta=24$.

System has a unique solution for $\alpha=-3, \beta=14$.

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