For the system of linear equations $x+y+z=6$ $\alpha x+\beta y+7 z=3$ $x+2 y+3 z=14$ which of the following is NOT true ?

Question

For the system of linear equations

$x+y+z=6$

$\alpha x+\beta y+7 z=3$

$x+2 y+3 z=14$

which of the following is NOT true ?

If $\alpha=\beta=7$, then the system has no solution

For every point $(\alpha, \beta) \neq(7,7)$ on the line $x-2 y+7=0$, the system has infinitely many solutions

There is a unique point $(\alpha, \beta)$ on the line $x+2 y+18=0$ for which the system has infinitely many solutions

If $\alpha=\beta$ and $\alpha \neq 7$, then the system has a unique solution

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