Question

Let α, β and γ be real numbers such that the system of linear equations
$x + 2y + 3z = α$
$4x + 5y + 6z = β$
$7x + 8y + 9z = γ – 1$
is consistent. Let$|M|$ represent the determinant of the matrix.
$M = \begin{bmatrix} \alpha & 2 & \gamma &\\\ \beta & 1 & 0 & \\\\-1& 0&1 \end{bmatrix}$
Let P be the plane containing all those $(α, β, γ)$ for which the above system of linear equations is consistent, and D be the square of the distance of the point (0, 1, 0) from the plane P.