System of Equations

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What is a system of equations?

Back

A system of equations is a set of two or more equations that have the same variables.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What does it mean if a system of equations has one solution?

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It means that the lines representing the equations cross at exactly one point.

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CCSS.8.EE.C.8A

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What does it mean if a system of equations has infinitely many solutions?

Back

It means that the lines representing the equations are the same, or coincide.

Tags

CCSS.8.EE.C.8B

Front

How can you determine if a system of equations has no solution?

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If the lines representing the equations are parallel, they will never intersect, indicating no solution.

Tags

CCSS.8.EE.C.8A

Front

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

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The graphical representation shows 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 infinitely many solutions?

Back

The graphical representation shows two lines that lie on top of each other.

Tags

CCSS.8.EE.C.8A

Front

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

Back

The graphical representation shows two parallel lines that never intersect.

Tags

CCSS.8.EE.C.8A

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What is the substitution method in solving systems of equations?

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The substitution method 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

The elimination method 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

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What is a consistent system of equations?

Back

A consistent system has at least one solution, which can be either one solution or infinitely many solutions.

Tags

CCSS.8.EE.C.8B