8.5 Systems of Equations

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system of equations

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A set of two or more equations with the same variables. A solution is an ordered pair that satisfies both equations. It can have one solution, infinite solutions, or no solution.

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consistent

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A system of equations is consistent if it has at least one ordered pair that satisfies both equations.

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independent

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A consistent system with exactly one solution. The graphs intersect at one point.

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dependent

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A consistent system with infinite solutions. The graphs are the same line, meaning unlimited solutions satisfy both equations.

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inconsistent

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A system with no ordered pair that satisfies both equations. The graphs are parallel.