Asked by Kim
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?
Answers
Answered by
Steve
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.
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.
Answered by
Steve
I guess the other possibility is that the lines are identical, so the solution set is everything on one side of the line.
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