Elimination Method Common Coefficients

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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 equations by eliminating one variable, allowing for the other variable to be solved directly.

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What does it mean if a system of equations has an infinite number of solutions?

Back

It means that the equations represent the same line, and thus every point on that line is a solution.

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What does it mean if a system of equations has no solution?

Back

It means that the equations represent parallel lines that never intersect, indicating that there are no common solutions.

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Define a system of equations.

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A system of equations is a set of two or more equations with the same variables that are solved together.

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How do you determine if a system of equations has one solution, no solution, or infinite solutions?

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By analyzing the slopes and intercepts of the lines represented by the equations: if they intersect, there's one solution; if they are parallel, there's no solution; if they are the same line, there are infinite solutions.

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Solve using the Elimination Method: x - y = 11 and 2x + y = 19.

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(10, -1)

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Solve using the Elimination Method: -4x - 4y = 0 and 4x + 4y = 0.

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Infinite number of solutions.

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What is the first step in the Elimination Method?

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

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If you have the equations 2x + 3y = 6 and 4x + 6y = 12, what can you conclude?

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These equations represent the same line, so there are infinite solutions.

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What is the purpose of the Elimination Method?

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To find the values of the variables that satisfy all equations in the system.