Systems of Equations

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What is a system of equations?

Back

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

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What does it mean to solve a system of equations?

Back

Finding the values of the variables that satisfy all equations in the system.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is a solution to a system of equations?

Back

A set of values for the variables that makes all equations true.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What is meant by 'no solution' in a system of equations?

Back

There are no values for the variables that satisfy all equations simultaneously.

Tags

CCSS.8.EE.C.8B

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What does 'infinitely many solutions' mean?

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There are countless sets of values that satisfy all equations in the system.

Tags

CCSS.8.EE.C.8B

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How can you determine if a system of equations has one solution?

Back

If the graphs of the equations intersect at exactly one point.

Tags

CCSS.8.EE.C.8A

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What is the graphical representation of a system of equations?

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The graphs of the equations plotted on the same coordinate plane.

Tags

CCSS.8.EE.C.8B

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What does it mean if two lines are parallel in a system of equations?

Back

The system has no solution because the lines never intersect.

Tags

CCSS.8.EE.C.8B

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What is the substitution method in solving systems of equations?

Back

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

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the elimination method in solving systems of equations?

Back

A method where equations are added or subtracted to eliminate one variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6