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 system of equations to have one solution?

Back

The lines representing the equations intersect at exactly one point.

Tags

CCSS.8.EE.C.8A

Front

What does it mean for a system of equations to have no solution?

Back

The lines representing the equations are parallel and never intersect.

Tags

CCSS.8.EE.C.8A

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

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

Tags

CCSS.8.EE.C.8A

Front

How do you solve a system of equations by elimination?

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You add or subtract the equations to eliminate one variable, making it easier to solve for the other.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the graphical representation of a system of equations with one solution?

Back

Two lines that intersect at a single point.

Tags

CCSS.8.EE.C.8A

Front

What is the graphical representation of a system of equations with no solution?

Back

Two parallel lines that never meet.

Tags

CCSS.8.EE.C.8A

Front

What is the graphical representation of a system of equations with infinitely many solutions?

Back

Two overlapping lines that lie on top of each other.

Tags

CCSS.8.EE.C.8A

Front

What is the solution of a system of linear equations?

Back

The point where the graphs of the equations intersect.

Tags

CCSS.8.EE.C.8A

Front

What is the elimination method?

Back

A method for solving systems of equations by removing one variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6