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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 no solution?

Back

It means that the equations represent parallel lines that never intersect.

Front

What is the elimination method in solving systems of equations?

Back

A technique where you add or subtract equations to eliminate one variable, making it easier to solve for the other.

Front

What is the substitution method in solving systems of equations?

Back

A method where you solve one equation for one variable and substitute that expression into the other equation.

Front

What is the graphing method for solving systems of equations?

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A method where you graph both equations on the same coordinate plane and find the point(s) where they intersect.

Front

What is the definition of a solution to a system of equations?

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A set of values for the variables that makes all equations in the system true.

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

Back

It means that the equations represent the same line, and there are countless points that satisfy both equations.

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How do you determine if a system of equations has one solution?

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If the lines represented by the equations intersect at exactly one point, the system has one solution.

Front

What is the purpose of the elimination method?

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To simplify the process of solving systems of equations by removing one variable.

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What is the first step in the substitution method?

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Solve one of the equations for one variable in terms of the other variable.