Systems of Equations Substitution & Elimination Method Flashcard

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

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What does it mean to solve a system of equations?

Back

Finding the values of the variables that satisfy all equations in the system.

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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.

Front

What is the elimination method?

Back

A method for solving systems of equations by adding or subtracting equations to eliminate one variable.

Front

What is 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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How do you check if a solution is correct?

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Substitute the values back into the original equations to see if they hold true.

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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.

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What is the first step in the elimination method?

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Align the equations and manipulate them to eliminate one variable.

Front

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

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The lines represented by the equations are parallel and never intersect.

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

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The equations represent the same line, meaning every point on the line is a solution.