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Systems of Linear Inequalities (page 2 of 2) The solution region for the previous example is called a "closed" or "bounded" solution, because there are lines on all sides. That is, the solution region is a bounded geometric figure (a triangle, in that case). You can also obtain solutions that are "open" or "unbounded"; that is, you will have some exercises which have solutions that go off forever in some direction. Here's an example:
2x
– y > –3
As usual, I first want to solve these inequalities for "y". I get the rearranged system: y
< 2x + 3
The kind of solution displayed in the above example is called "unbounded", because it continues forever in at least one direction (in this case, forever downward). Of course, there's always the possibility of getting no solution at all. For instance:
x
– y < –2
First I solve for y, and get the equivalent system: y
> x + 2
But there is no place where the individual solutions overlap. (Note that the lines y = x + 2 and y = x – 2 never intersect, being parallel lines with different yintercepts.) Since there is no intersection, there is no solution. << Previous Top  1  2  Return to Index



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