elimination method!!!

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What is the elimination method in solving systems of equations?

Back

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 combine two equations in the elimination method?

Back

To combine two equations, you can add or subtract them after multiplying one or both equations by a suitable number to align coefficients of one variable.

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What is a zero pair in the context of the elimination method?

Back

A zero pair occurs when two terms in an equation cancel each other out, resulting in a sum of zero, which helps in eliminating a variable.

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What is the first step in using the elimination method?

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The first step is to arrange the equations in standard form (Ax + By = C) and identify which variable to eliminate.

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When is it necessary to multiply an equation in the elimination method?

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It is necessary to multiply an equation when the coefficients of the variable you want to eliminate are not opposites, allowing you to create a zero pair.

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What does it mean to eliminate a variable?

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To eliminate a variable means to manipulate the equations so that one variable is removed, allowing for the solution of the other variable.

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What is the resulting equation when combining 5x - 4y = 11 and 5x + 4y = -14?

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The resulting equation is 10x = -3.

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How do you determine which variable to eliminate in a system of equations?

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You can choose to eliminate the variable that has the same or easily manipulable coefficients in both equations.

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What is the significance of the coefficients in the elimination method?

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Coefficients determine how the equations can be manipulated to create zero pairs for variable elimination.

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What is the resulting equation when combining 9x + y = 12 and -9x + y = 6?

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The resulting equation is 2y = 18.