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

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How do you eliminate a variable in a system of equations?

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To eliminate a variable, you can add or subtract the equations in such a way that one variable cancels out.

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

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An infinite number of solutions 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?

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No solution means that the equations represent parallel lines that never intersect.

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Solve the system using Elimination Method: 2x + 3y = 6 and 4x + 6y = 12.

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Infinite number of solutions.

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Solve the system using Elimination Method: x + y = 5 and x - y = 1.

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(3, 2).

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What is the first step in using the Elimination Method?

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The first step is to align the equations and decide which variable to eliminate.

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How can you make the coefficients of a variable equal in two equations?

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You can multiply one or both equations by a number to make the coefficients of the variable you want to eliminate equal.

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Solve using Elimination Method: 3x + 2y = 12 and 3x - y = 3.

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(3, 0).

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What is a key advantage of the Elimination Method over substitution?

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The Elimination Method can be more efficient for systems with complex equations or when both equations are already aligned.