Will a 4" non-reinforced concrete slab support my swimming pool?
Concrete is usually rated at 3,000 or more PSI, which is a measure of crush resistance. You won't come anywhere near that. So the question becomes one of crack resistance, and that's going to depend almost entirely on the integrity of the substrate. 

If it was poured directly on organic soil, it'll probably crack. If it's on a good base of gravel, sand, or recycled concrete, it'll probably hold well. Really, though, a crack won't change the slab's ability to support the pool. I'd assume that the pool will be placed on a mat of some sort that would protect it against any edges or irregularities in the concrete. 



Some calculations (which are approximate, but close enough to allow us to dismiss outright crush strength as a concern):


  7ft * 10ft = 70 sq ft
  70 sq ft * 144 sq in = 10,080 sq in
  17,458 lbs / 10,080 sq in = 1.7319 PSI


As you can see, crush resistance isn't a concern. It's all about whether the slab has to span any weak areas in the substrate, which could result in cracks and surface offset.