Official solution
The equation of any plane passing through the intersection of the planes 2x -- y -- 4 = 0 and
y + 2z -- 4 = 0 is :
(2x -- y -- 4) + \[\lambda (y + 2z -- 4) = 0 ........(1)
As this plane passes through (1, 1, 0) then this point satisfy the equation (1).
\[ \therefore \] (2 -- 1 -- 4) + \[\lambda (1 + 0 -- 4) = 0
\[ \Rightarrow \] \[\lambda \] = -1
Equation of required plane will be
(2x -- y -- 4) -- (y + 2z -- 4) = 0
\[ \Rightarrow \] 2x -- 2y -- 2z = 0
\[ \Rightarrow \] x -- y -- z = 0