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When the determinant of the coefficient matrix of a system of equations does not equal zero, the system has _________ solution(s)?
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http://math.oregonstate.edu/home/programs/undergrad/CalculusQuestStudyGuides/vcalc/system/system.html The section labeled "Determining the Number of Solutions of a Nonhomogeneous System of Equations" explains it. But to answer your question, there would be only one solution. In the case of a determinant that is zero, it would have infinite solutions.
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