Systems of Linear Equations

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What is a system of linear equations?

Back

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 for a point to be a solution to a system of equations?

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It means that the point satisfies all equations in the system.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What are the three main methods to solve systems of linear equations?

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Graphing, Substitution, and Elimination.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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How do you determine if a point is a solution to a system of equations?

Back

Substitute the point's coordinates into each equation and check if they hold true.

Front

What is the elimination method?

Back

A method for solving systems of equations by adding or subtracting equations to eliminate a variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the substitution method?

Back

A method for solving systems of equations by solving one equation for a variable and substituting that expression into the other equation.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What does it mean if two lines intersect at a point on a graph?

Back

It means that the system of equations has one unique solution.

Tags

CCSS.8.EE.C.8A

Front

What does it mean if two lines are parallel on a graph?

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It means that the system of equations has no solution.

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CCSS.8.EE.C.8A

Front

What does it mean if two lines coincide on a graph?

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It means that the system of equations has infinitely many solutions.

Tags

CCSS.8.EE.C.8A

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How can you represent a real-world situation with a system of equations?

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By defining variables for the quantities involved and writing equations based on relationships between those quantities.

Tags

CCSS.8.EE.C.8C