No Solution/Infinite Solution/One Solution

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What does it mean if an equation has one solution?

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An equation has one solution when there is exactly one value of the variable that satisfies the equation.

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What does it mean if an equation has no solution?

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An equation has no solution when there is no value of the variable that can satisfy the equation, often resulting in a contradiction.

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What does it mean if an equation has infinitely many solutions?

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An equation has infinitely many solutions when any value of the variable satisfies the equation, typically when both sides of the equation are equivalent.

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One solution: n = 1.

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One solution: x = 0.

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One solution: x = 2.

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One solution: m = -1.

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Infinitely many solutions.

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What is a contradiction in an equation?

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A contradiction occurs when simplifying an equation leads to a false statement, indicating no solution exists.

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What is a dependent equation?

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A dependent equation is one that has infinitely many solutions, often because it simplifies to an identity.