Official solution
Given,
x + 8y + 7z = 0
9x + 2y + 3z = 0
x + y + z = 0
Solving those equations, we get
x = \[\lambda \], y = 6\[\lambda \], z = -7\[\lambda \]
This point lies on the plane x + 2y + z = 6
\[ \therefore \] \[\lambda \] + 2(6\[\lambda \]) + (-7\[\lambda \]) = 0
\[ \Rightarrow \] \[\lambda \] = 1
\[ \therefore \] x = 1, y = 6, z = -7
\[ \therefore \] a = 1, b = 6, c = -7
So, 2a + b + c = 2(1) + 6 + (-7) = 1