Wednesday, September 18, 2013

How many solution sets do systems of linear inequalities have? Do Solutions to systems of linear inequalities need to satisfy both inequalities? In What case might they not?

A solution set may have any number of solutions, the most common answers for this are; 0,1 or infinite. An example where only one is had is when x≤3 and x≥3. An example of a solution where none are found is when given x>3 and x<2. Both of these cannot be satisfied at the same time, so there is no solution set for this number. If a system does not fit into both of the inequalities and the word “and” is used, there will be no solutions to the given problem. The last option is when you are given something like x>3 and x>4. This is a solution where any number greater than 4 will satisfy the conditions, and will be considered infinite. 

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