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 linear equations to have one solution?

Back

It means that the lines represented by 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 linear equations to have no solution?

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It means that the lines represented by the equations are parallel and never intersect.

Tags

CCSS.8.EE.C.8A

Front

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

Back

It means that the lines represented by the equations coincide, or are the same line.

Tags

CCSS.8.EE.C.8A

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

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What is the substitution method?

Back

A method for solving systems of equations by solving one equation for one variable and substituting that expression into the other equation.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the graphical method for solving systems of equations?

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A method that involves graphing the equations on a coordinate plane and identifying the point(s) of intersection.

Tags

CCSS.8.EE.C.8B

Front

How do you write an ordered pair?

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An ordered pair is written as (x, y), where x is the value of the first variable and y is the value of the second variable.

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CCSS.8.F.A.1

CCSS.HSF.IF.B.5

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What is the standard form of a linear equation?

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The standard form is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

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What is the slope-intercept form of a linear equation?

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The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3