Types of Solutions

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What is a solution in mathematics?

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A solution is a value or set of values that satisfy an equation or inequality.

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What does it mean if an equation has one solution?

Back

It means there is exactly one value that makes the equation true.

Tags

CCSS.8.EE.C.7A

Front

What does it mean if an equation has no solution?

Back

It means there is no value that can satisfy the equation.

Tags

CCSS.8.EE.C.7A

Front

What does it mean if an equation has infinite solutions?

Back

It means there are countless values that satisfy the equation, often because the equation is an identity.

Tags

CCSS.8.EE.C.7A

Front

Example of an equation with infinite solutions: x + 2 = x + 2. What is the solution?

Back

Infinite solutions.

Tags

CCSS.8.EE.C.7A

Front

Example of an equation with no solution: x + 3 = x - 2. What is the solution?

Back

No solution.

Tags

CCSS.8.EE.C.7A

Front

What is a linear equation?

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An equation that makes a straight line when graphed, typically in the form y = mx + b.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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What is the graphical representation of an equation with one solution?

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Two lines intersecting at a single point.

Tags

CCSS.8.EE.C.8A

Front

What is the graphical representation of an equation with no solution?

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Two parallel lines that never intersect.

Tags

CCSS.8.EE.C.8A

Front

What is the graphical representation of an equation with infinite solutions?

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Two overlapping lines that are identical.