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?\\
(1) The system has infinitely many solutions for $\alpha = -5$ and $\beta = 9$\\
(2) The system has infinitely many solutions for $\alpha = -6$ and $\beta = 9$\\
(3) The system is inconsistent for $\alpha = -5$ and $\beta = 8$\\
(4) The system has a unique solution for $\alpha \neq -5$ and $\beta = 8$