The first way to tell if a quadratic has no real solution is to look at the discriminant. If the discriminant is negative, then the quadratic equation has no real solution. The discriminant is
How to tell if a linear equation has one solution, no solution, or infinitely many solutions.
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If (a 1 /a 2) = (b 1 /b 2) ≠ (c 1 /c 2), then there will be no solution. This type of equation is called an inconsistent pair of linear equations. If we plot the graph, the lines will be parallel. The graph is
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