For the system of linear equations $2x - y + 3z = 5$ $3x + 2y - z = 7$ $4x + 5y + \alpha z = \beta $, which of the following is NOT correct?

Question

For the system of linear equations

$2x - y + 3z = 5$

$3x + 2y - z = 7$

$4x + 5y + \alpha z = \beta $,

which of the following is NOT correct?

The system has infinitely many solutions for $\alpha=-6$ and $\beta=9$

The system has a unique solution for $\alpha$ $ \ne $ $-5$ and $\beta=8$

The system is inconsistent for $\alpha=-5$ and $\beta=8$

The system has infinitely many solutions for $\alpha=-5$ and $\beta=9$

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