Identifying Solutions to Systems of Equations

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What is a system of equations?

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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 for a system of equations to have a unique solution?

Back

It means there is exactly one set of values for the variables that satisfies all equations in the system.

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CCSS.8.EE.C.8B

Front

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

Back

It means there are no values for the variables that can satisfy all equations in the system.

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CCSS.8.EE.C.8B

Front

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

Back

It means there are an unlimited number of values for the variables that satisfy all equations in the system.

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CCSS.8.EE.C.8B

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

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By checking if the lines represented by the equations intersect at exactly one point.

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CCSS.8.EE.C.8A

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What is the graphical representation of a system of equations?

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It is represented by the graphs of the equations on the same coordinate plane.

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CCSS.8.EE.C.8B

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What is the substitution method in solving systems of equations?

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It involves 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

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What is the elimination method in solving systems of equations?

Back

It involves adding or subtracting 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 slope-intercept form of a linear equation?

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It is written as y = mx + b, where m is the slope and b is the y-intercept.

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CCSS.8.EE.B.6

CCSS.8.F.A.3

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

Back

It means they have the same slope but different y-intercepts, resulting in no solutions.

Tags

CCSS.8.EE.C.8B