I think for a system to be officially logged it needs 5 distances entered from 5 different locations, so its exact location in the galaxy can be pinpointed.
It needs *enough* distances. 5 might suffice - 3 might be enough if you're lucky, but it might be more, it depends.
If you have a known point in 3D space and a defined distance to an unknown position then the distance puts the unknown point on a sphere. If you have three points and three distances then theoretically you have three spheres which intersect at a single point in space which is where the unknown point must reside.
Unfortunately our distances are measured to a hundredth of a light year but the positions are snapped to a 32nd of a light year grid so the spheres are shells a hundredth of a light year thick and three usually defines a volume with multiple valid coordinates.
Every distance from a new known point shrinks that volume and restricts the number of valid coordinates until there's only one left.
5 or 6 is often sufficient, if they're widely spaced. If they're all on pretty much the same straight line then it can take many more (back when we had to trilaterate everything I had systems that still weren't well located after 40 or 50 distances, given the flat nature of the galaxy the vertical coordinate is often least well defined).
Shameless plug -
ED Discovery has a tab for bulk entry of distances and pulls the priority systems from EDSM to allow you to quickly enter distances if you want to help. It also allows you to save your own local list of systems you want to fix, say to fill in your own travel maps (and EDSM will automatically start pushing those to the front if you've entered a number of distances and not got a fix yet).
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