Solving Systems of Linear Equations with Elimination

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What is a system of linear equations?

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

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What does it mean to solve a system of linear equations?

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

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What is the elimination method?

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A technique for solving systems of linear equations by eliminating one variable to solve for the other.

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

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By adding or subtracting the equations to cancel out one of the variables.

Front

What is the first step in using the elimination method?

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

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

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

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What is a consistent system of equations?

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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 after solving a system of equations?

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