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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What is the first step in using the Elimination Method?

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The first step is to manipulate the equations to align coefficients of one variable so that they can be eliminated when the equations are added or subtracted.

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How do you create a zero pair in the Elimination Method?

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To create a zero pair, you multiply one or both equations by a number so that the coefficients of one variable are opposites, allowing them to cancel each other out.

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What does it mean to 'cross out' a variable in the Elimination Method?

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'Crossing out' a variable means to eliminate it from the equations by adding or subtracting the equations, resulting in a single equation with one variable.

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In the equation 4x + 3y = 1 and x - 3y = -11, which variable can be eliminated first?

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The variable 3y can be eliminated by aligning the coefficients of y in both equations.

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What is the solution to the system of equations x - y = 11 and 2x + y = 19 using the Elimination Method?

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The solution is (10, -1).

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What is a 'zero pair' in the context of the Elimination Method?

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

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

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You can determine which variable to eliminate by looking for the variable with coefficients that can easily be manipulated to create opposites.

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What is the purpose of multiplying an equation in the Elimination Method?

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Multiplying an equation is done to adjust the coefficients of a variable so that they can be eliminated when the equations are combined.

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What is the result of eliminating a variable in a system of equations?

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The result is a single equation with one variable, which can be solved to find the value of that variable.