Line of intersection between two planes?

what is the equation of the line formed by the intersection of two planes x + y + z = 1 x + y = 0 i was told you have to find the cross product and then find a point that satisfied both equations. I got (-1, 1, 0) as my normal vector. the vector normal to both planes. however, when I try to find a point, I can't. I set z = 0 and then I get x + y = 1 x + y = 0 which does not work? what am I doing wrong?