One Solution, No Solution, Infinite Solutions

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What are the three types of solutions for a system of equations?

Back

One Solution, No Solution, Infinite Solutions.

Tags

CCSS.8.EE.C.8B

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What does it mean if a system of equations has 'No Solution'?

Back

It means that the equations represent parallel lines that never intersect.

Tags

CCSS.8.EE.C.8A

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What does it mean if a system of equations has 'One Solution'?

Back

It means that the equations represent lines that intersect at exactly one point.

Tags

CCSS.8.EE.C.8A

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What does it mean if a system of equations has 'Infinite Solutions'?

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It means that the equations represent the same line, so every point on the line is a solution.

Tags

CCSS.8.EE.C.8B

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How can you determine if a system of equations has 'No Solution'?

Back

If the equations simplify to a contradiction, such as 0 = 5, then there is no solution.

Tags

CCSS.8.EE.C.8B

Front

How can you determine if a system of equations has 'One Solution'?

Back

If the equations simplify to a true statement with a unique solution for the variable, then there is one solution.

Tags

CCSS.8.EE.C.8B

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How can you determine if a system of equations has 'Infinite Solutions'?

Back

If the equations simplify to an identity, such as 0 = 0, then there are infinite solutions.

Tags

CCSS.8.EE.C.8B

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What is an example of a system of equations with 'No Solution'?

Back

y = 2x + 1 and y = 2x - 3 are parallel lines, hence no solution.

Tags

CCSS.8.EE.C.8B

Front

What is an example of a system of equations with 'One Solution'?

Back

y = 2x + 1 and y = -x + 3 intersect at one point, hence one solution.

Tags

CCSS.8.EE.C.8B

Front

What is an example of a system of equations with 'Infinite Solutions'?

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2x + 4 = 2(x + 2) represents the same line, hence infinite solutions.

Tags

CCSS.8.EE.C.8B