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

Front

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

Back

The lines representing the equations are parallel and never intersect.

Tags

CCSS.8.EE.C.8A

Front

What is the graphical representation of intersecting lines?

Back

It indicates that the system of equations has a unique solution.

Tags

CCSS.8.EE.C.8A

Front

What is the solution of a system of equations?

Back

The point where the graphs of the equations intersect.

Tags

CCSS.8.EE.C.8B

Front

What does ARN stand for in the context of systems of equations?

Back

All Real Numbers; it indicates that the equations represent the same line.

Tags

CCSS.8.EE.C.8B

Front

How do you determine if a system of equations has infinitely many solutions?

Back

If the equations represent the same line, they have infinitely many solutions.

Tags

CCSS.8.EE.C.8B

Front

What is the substitution method in solving systems of equations?

Back

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

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

Front

What is the significance of the coefficients in a linear equation?

Back

They determine the slope and position of the line on a graph.

Front

How can you tell if two lines are parallel from their equations?

Back

If their slopes (coefficients of x) are equal and their y-intercepts are different.

Tags

CCSS.8.EE.B.6