For the system of linear equations \(\begin{aligned}& 2 x-y+3 z=5 \\& 3 x+2 y-z=7 \\& 4 x+5 y+\alpha z=\beta…

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

The system has a unique solution for \(\alpha \neq-5\) and \(\beta=8\)

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

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