List of top Mathematics Questions on System of Linear Equations asked in JEE Main

Let for any three distinct consecutive terms $a, b, c$ of an A.P., the lines $ax + by + c = 0$ be concurrent at the point $P$ and $Q (\alpha, \beta)$ be a point such that the system of equations $$x + y + z = 6,$$$$2x + 5y + \alpha z = \beta,$$$$x + 2y + 3z = 4,$$has infinitely many solutions. Then $(PQ)^2$ is equal to ______.

If the system of equations
$2x + 3y - z = 5$  
$x + \alpha y + 3z = -4$  
$3x - y + \beta z = 7$  
has infinitely many solutions, then $13 \alpha \beta$ is equal to: