Solving Systems by Elimination

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.

Front

What is the elimination method?

Back

A technique for solving systems of equations by adding or subtracting equations to eliminate a variable.

Front

How do you eliminate a variable in a system of equations?

Back

By manipulating the equations so that when added or subtracted, one variable cancels out.

Front

What is the first step in the elimination method?

Back

Align the equations so that corresponding variables and constants are in the same columns.

Front

What do you do if the coefficients of a variable are not the same?

Back

Multiply one or both equations by a number to make the coefficients equal.

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What is a consistent system of equations?

Back

A system that has at least one solution.

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What is an inconsistent system of equations?

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A system that has no solutions.

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What is a dependent system of equations?

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A system that has infinitely many solutions, where the equations represent the same line.

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

Back

By substituting the solution back into the original equations to see if they hold true.