Systems of Linear Equations

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What is a system of linear equations?

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A set of two or more linear equations with the same variables.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What does it mean if two lines intersect at one point when graphing a system of linear equations?

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The system has one unique solution.

Tags

CCSS.8.EE.C.8A

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What does it mean if two lines are parallel when graphing a system of linear equations?

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The system has no solution.

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CCSS.8.EE.C.8B

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What does it mean if two lines overlap when graphing a system of linear equations?

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The system has infinite solutions.

Tags

CCSS.8.EE.C.8A

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What is the elimination method in solving systems of linear equations?

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A method that involves adding or subtracting equations to eliminate one variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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Solve by elimination: 2x + 3y = 6 and 4x + 6y = 12. What is the solution?

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Infinite solutions.

Tags

CCSS.8.EE.C.8B

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Solve by elimination: x + y = 5 and x - y = 1. What is the solution?

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(3, 2).

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What is the substitution method in solving systems of linear equations?

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A method where one equation is solved for one variable, and then substituted into the other equation.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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Solve by substitution: y = 2x + 1 and 3x - y = 4. What is the solution?

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(1, 3).

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.

Tags

CCSS.8.EE.C.8B