no they can't
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No. Ray= A finite beginning and no finite end. A ray is a linear projection in one direction. If three rays begin at the same point of origin they will never intersect again given their respective directions. Same goes for the situation of them beginning at different P.O.O's; it's only physically possible for them to intersect at one point then after. (Unless of course you bring into the picture mirrors and different mediums wherein the index could possibly cause them to reflect/refract and change their paths.. then they could possibly intersect at more than one point... BUT generally/simply speaking NO three rays cannot intersect at more than one point :-) )
Sometimes. Not always.
Yes. Any two distinct lines of longitude, for example, meet at two points - the poles. On a plane, though, two points define a unique line. So if two lines intersect at more than one point they must be coincident.
No. A linear equation represents a straight line and the solution to a set of linear equations is where the lines intersect; two straight lines can only intersect at most at a single point - two straight lines may be parallel in which case they will not intersect and there will be no solution. With more than two linear equations, it may be that they do not all intersect at the same point, in which case there is no solution that satisfies all the equations together, but different solutions may exist for different subsets of the lines.
No because the 2 straight lines can only intersect one another at one particular point