Systems of Equations: Choosing the Best Method

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What is a system of equations?

Back

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

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean if a system of equations has one solution?

Back

The lines representing the equations intersect at exactly one point.

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CCSS.8.EE.C.8A

Front

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

Back

The lines representing the equations are parallel and never intersect.

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CCSS.8.EE.C.8A

Front

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

Back

The lines representing the equations coincide, meaning they are the same line.

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CCSS.8.EE.C.8A

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What is the substitution method?

Back

A method for solving systems of equations where one equation is solved for one variable, and that expression is substituted into the other equation.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the elimination method?

Back

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

Front

What is the equal values method?

Back

A method for solving systems of equations where both equations are set equal to each other to find the variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

When is the substitution method most useful?

Back

When one equation is already solved for one variable or can be easily manipulated to do so.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

When is the elimination method most useful?

Back

When the coefficients of one variable are the same or can be easily made the same.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the first step in solving a system of equations using elimination?

Back

Align the equations so that like terms are in the same column.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6