Number Of Solutions to Equations

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What is the definition of a linear 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. This often occurs when two lines are parallel.

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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. This occurs when two equations represent the same line.

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The equation has infinitely many solutions because both sides are identical.

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What is the significance of the slope in a linear equation?

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The slope indicates the steepness of the line and the direction it moves. A positive slope means the line rises, while a negative slope means it falls.

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What does it mean if two equations are inconsistent?

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Two equations are inconsistent if they do not intersect at any point, meaning they have no solutions.

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The equation has infinitely many solutions because both sides are identical.