No Solution, One Solution, Infinite Solutions

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What does it mean if an equation has Infinite Solutions?

Back

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.

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What does it mean if an equation has No Solution?

Back

An equation has no solution when there is a contradiction in the equation, meaning no value of the variable can satisfy it.

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What does it mean if an equation has One Solution?

Back

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

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

Back

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

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

Back

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

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

Back

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

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

Back

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

Back

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

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What is a contradiction in an equation?

Back

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

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How can you identify an equation with Infinite Solutions?

Back

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