INTRO 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.

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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.

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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 can you determine if a system of equations has one solution, no solution, or infinitely many solutions?

Back

By graphing the equations and observing the intersection points.

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CCSS.8.EE.C.8B

Front

What is the solution to the system of equations: y = 2x + 1 and y = -x + 4?

Back

(1, 3)

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the solution to the system of equations: 2x + 3y = 6 and x - y = 1?

Back

(3, 0)

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the graphical representation of a system of equations?

Back

It is represented by lines on a coordinate plane.

Tags

CCSS.8.EE.C.8A

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