Systems of Equations

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What is a system of equations?

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A set of two or more equations that have the same variables.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What does it mean if a system of equations has infinitely many solutions?

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It means that there are an infinite number of ordered pairs that satisfy all equations in the system.

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CCSS.8.EE.C.8B

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What is the solution of a system?

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The ordered pair that satisfies all equations in the system.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What does the graph of a system with no solution look like?

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The graph consists of parallel lines.

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CCSS.8.EE.C.8A

Front

What is one solution in a system of equations?

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It is a unique ordered pair that satisfies all equations in the system.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What is the elimination method?

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A method for solving systems of equations by eliminating one variable to solve for the other.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What is a consistent system of equations?

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A system that has at least one solution.

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CCSS.8.EE.C.8B

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What is an inconsistent system of equations?

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A system that has no solutions.

Tags

CCSS.8.EE.C.8B

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What does it mean for two lines to be intersecting in a graph of a system of equations?

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It means that the system has exactly one solution, represented by the point of intersection.

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CCSS.8.EE.C.8A

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How can you determine if a system of equations has no solution?

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If the equations represent parallel lines, they will never intersect, indicating no solution.

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CCSS.8.EE.C.8A