elimination method!!!

Front

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.

Front

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.

Front

In the elimination method, what does it mean to create a zero pair?

Back

Creating a zero pair means manipulating the equations so that when they are added together, one variable cancels out, resulting in an equation with only one variable.

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What is the first step in using the elimination method?

Back

The first step is to align the equations and decide which variable to eliminate, then manipulate the equations (by multiplying if necessary) to create coefficients that will cancel out.

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

Back

You can determine which variable to eliminate by looking at the coefficients of the variables in both equations and choosing the one that can be easily manipulated to create a zero pair.

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What do you do if the coefficients of the variable you want to eliminate are not the same?

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If the coefficients are not the same, you can multiply one or both equations by a number to make the coefficients equal.

Front

What is the result of adding the equations 5x - 4y = 11 and 5x + 4y = -14?

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The result is 10x = -3.

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What is the purpose of multiplying an equation in the elimination method?

Back

Multiplying an equation is done to adjust the coefficients of the variables so that when the equations are added or subtracted, one variable cancels out.

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What happens if both variables are eliminated in the elimination method?

Back

If both variables are eliminated, it may indicate that the system has either no solution (inconsistent) or infinitely many solutions (dependent).

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What is a common mistake when using the elimination method?

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A common mistake is failing to correctly multiply the equations, leading to incorrect coefficients and ultimately an incorrect solution.