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What is the nature of intersection of these three planes:

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?

2 answers

correction, the two planes are coincident that the other intersects in line
unless the normals are parallel, the planes must intersect in a line.
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