which lines indicate no solution.
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Since parallel lines never cross, then there can be no intersection; that is, for a system of equations that graphs as parallel lines, there can be no solution. This is called an "inconsistent" system of equations, and it has no solution.
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A system has no solutions if the lines are parallel. When solving the system, if you get a false statement (a number equal to a different number) this means there are no solutions.
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