Systems of Equations

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

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

Back

The graphs of the equations intersect at exactly one point.

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

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The graphs of the equations are parallel and never intersect.

Front

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

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The graphs of the equations are the same line, meaning they intersect at every point.

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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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.

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What is the graphing method?

Back

A method for solving systems of equations by graphing the equations and finding the point(s) of intersection.

Front

What is the first step in solving a system of equations using the elimination method?

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Align the equations so that like terms are in the same column.

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How can you check if your solution to a system of equations is correct?

Back

Substitute the solution back into the original equations to see if both equations are satisfied.

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What is a consistent system of equations?

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A system that has at least one solution.