Elimination Method

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What is the Elimination Method in solving systems of equations?

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The Elimination Method is a technique used to solve systems of linear equations by eliminating one variable, allowing for the solution of the remaining variable.

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

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To eliminate a variable, you can multiply one or both equations by a number so that the coefficients of one variable are opposites, allowing you to add or subtract the equations.

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What is the first step in using the Elimination Method?

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The first step is to align the equations and decide which variable to eliminate.

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What do you do after eliminating one variable in a system of equations?

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After eliminating one variable, solve for the remaining variable, then substitute back to find the value of the eliminated variable.

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What is a consistent system of equations?

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A consistent system of equations has at least one solution.

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What is an inconsistent system of equations?

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An inconsistent system of equations has no solutions.

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What is a dependent system of equations?

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A dependent system of equations has infinitely many solutions, as the equations represent the same line.

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How can you check your solution after using the Elimination Method?

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You can check your solution by substituting the values back into the original equations to see if they hold true.

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What is the significance of the coefficients in the Elimination Method?

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The coefficients determine how you can manipulate the equations to eliminate variables effectively.

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What happens if the coefficients of the variable you want to eliminate are already opposites?

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If the coefficients are already opposites, you can directly add the equations to eliminate that variable.