Solving Systems by Elimination

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What is a system of equations?

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A set of two or more equations with the same variables that are solved together.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What does it mean to solve a system by elimination?

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It means to eliminate one variable by adding or subtracting the equations, allowing you to solve for the other variable.

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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 adding or subtracting equations to eliminate one variable.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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How do you determine if a system of equations has a unique solution?

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If the lines represented by the equations intersect at exactly one point, the system has a unique solution.

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CCSS.8.EE.C.8A

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What does it mean if a system of equations has no solution?

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It means the lines represented by the equations are parallel and never intersect.

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CCSS.8.EE.C.8A

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

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It means the equations represent the same line, so there are an infinite number of points that satisfy both equations.

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CCSS.8.EE.C.8A

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(-1, -4)

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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(3, -2)

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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(1, 3)

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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(7, 0)

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6