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how can I determine if a linear system has infinite number of solutions, only one, or none?
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If the system can be solved for unique values of x, y, and z respectively, then it has one solution. If you can manipulate the system so it produces the statement 0=0 then it has infinite solutions. If you can manipulate the system so that is says a falsehood, like 1=2, the system has no solutions.
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