7.3 Practice (Solving Systems of Equations: 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 determine if a system of equations has no solution?

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A system of equations has no solution if the lines represented by the equations are parallel, meaning they have the same slope but different y-intercepts.

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What does it mean if a system of equations has infinitely many solutions?

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A system has infinitely many solutions if the equations represent the same line, meaning every point on the line is a solution.

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The solution is (-6, -1).

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Back

The solution is (3, 2).

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Back

The system has no solution.

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The solution is (4, 7).

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The solution is (1, -2).

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What is the first step in the Elimination Method?

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The first step is to align the equations and manipulate them (by multiplying or adding) to eliminate one variable.

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What is the significance of the coefficients in the Elimination Method?

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The coefficients determine how the equations can be manipulated to eliminate a variable; they must be adjusted to match in magnitude.