What is the nature of intersection of these three planes:

Question

5x+3y-z=11
-2x-7y+10z=2
6x+21y-30z=-6

I know that the answer is two parallel planes and the other one intersecting in a line. my question is how would you know that the first equation intersects in a line? Would you use elementary operations?

Answer 1

correction, the two planes are coincident that the other intersects in line

Answer 2

unless the normals are parallel, the planes must intersect in a line.