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 other variable to be solved directly.

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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 do you need to multiply an equation by to create a zero pair?

Back

You need to multiply the equation by a coefficient that will make the coefficients of one variable equal and opposite in both equations.

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What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

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How do you determine if two equations can be solved using the elimination method?

Back

Both equations should be in standard form, and at least one variable's coefficients should be able to be made equal and opposite.

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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 (by multiplying or adding) to align the coefficients of one variable.

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If you have the equations 5x - 2y = 11 and -10x + 3y = -4, what do you multiply the first equation by to eliminate x?

Back

Multiply the first equation by 2.

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What happens if there is no zero pair to eliminate in the elimination method?

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If there is no zero pair, it may indicate that the system of equations has no solution or infinitely many solutions.

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What is the result of combining the equations -2x + 6y = -20 and 2x + 5y = -11?

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The combined resulting equation is 11y = -31.

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What does it mean if two equations are dependent?

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Dependent equations are those that represent the same line, leading to infinitely many solutions.