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How many solution sets do systems of linear inequalities have?
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A system of linear inequalities can have none, one, or an infinite number of solutions; therefore, there are three.
In order for a number to be a solution to a linear inequality it must satisfy all linear inequalities. For example, in a system with two linear inequalities:
This has no solutions: x>7 and x<4 because a number cannot be greater than 7 AND less than 4
This has one solution: x>=7 and x<=7 because the only value that satisfies both inequalities is 7
This has an infinite number of solutions: x>1 and x>2 because all numbers greater than 2 satisfy both inequalities
Posted by crmhaske on May 16, 2013 at 2:56 AM (Answer #1)
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