How many solution sets do systems of linear inequalities have? Do solutions to systems of linear inequalities need to satisfy both inequalities? If so what are some examples?

Answer 1

Solution sets are regions which lie on one side of each line.

If the lines are parallel, the solution set will either be

between the lines (as in -3 < x < 5)
a single region (as in x>2 and x>5)
empty (as in x<4 and x>6)

Note that since we are dealing with a set of inequalities, they are connected with AND, so they must all be satisfied.

If the lines are not parallel, then they intersect. The solution set will be everything in one of the regions with the two lines as boundary.

Answer 2

I guess the other possibility is that the lines are identical, so the solution set is everything on one side of the line.