The point of intersection of the line passing through (0,0,1) and intersecting the lines x+2y+z=1,−x+y−2z=2 and x+y=2,x+z=2 with xy plane is

Equation of line. x+2y+z−1+λ(−x+y−2z−2)=0-----ix+y−2+μ(x+z−2)=0----ii(0,0,1) lies on it ⇒λ=0,μ=−2 For point of intersection, z=0 and solve (i) and (ii).