No Solution, One Solution, Infinite Solutions

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What does it mean if an equation has Infinite Solutions?

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An equation has infinite solutions when both sides of the equation are identical for all values of the variable, meaning any value will satisfy the equation.

Tags

CCSS.8.EE.C.7A

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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 a contradiction in the equation, meaning no value of the variable can satisfy it.

Tags

CCSS.8.EE.C.7A

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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 makes the equation true.

Tags

CCSS.8.EE.C.7B

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Example of an equation with Infinite Solutions: -10y-6 = -10y-6

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This equation is true for all values of y, hence it has infinite solutions.

Tags

CCSS.8.EE.C.7A

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Example of an equation with No Solution: 9y+8=9y-8

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This equation simplifies to 8 = -8, which is a contradiction, hence it has no solution.

Tags

CCSS.8.EE.C.7A

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Example of an equation with No Solution: 5y-15=5(y-2)

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This equation simplifies to -15 = -10, which is a contradiction, hence it has no solution.

Tags

CCSS.8.EE.C.7A

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Example of an equation with One Solution: 6(m+3)=5(m-2)

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This equation simplifies to 6m + 18 = 5m - 10, leading to m = -28, hence it has one solution.

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Example of an equation with Infinite Solutions: 3(x-8)=3x-24

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This equation simplifies to 3x - 24 = 3x - 24, which is true for all x, hence it has infinite solutions.

Tags

CCSS.8.EE.C.7A

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What is a contradiction in an equation?

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A contradiction occurs when an equation simplifies to a false statement, indicating that no values satisfy the equation.

Tags

CCSS.8.EE.C.7A

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How can you identify an equation with Infinite Solutions?

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If after simplifying the equation, both sides are identical, it indicates infinite solutions.

Tags

CCSS.8.EE.C.7A