The three planes x+y=0,y+z=0  and  x+z=0

The planes x+y=0 i.e. x=−y  and y+z=0 i.e. z=−y  meet in the line x1=y−1=z1 .any point on this line is (t,−t,t) .  This point lies in the plane x+z=0 if  t+t=0 ⇒t=0 . So the three planes meet in a unique point (0,0,0)ALTERNATE:The equation x+y=0,y+z=0 and z+x=0 has no non trivial solution as|110011101|≠0 . So only x=y=z=0 satisfies the given equations.