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 linear equations by eliminating one variable, allowing for the solution of the remaining variable.

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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 of the variables 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 is the graphical interpretation of the solution to a system of equations?

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The solution to a system of equations is the point where the graphs of the equations intersect.

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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 manipulate them to make the coefficients of one variable the same.

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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.

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

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You can multiply one or both equations by a suitable number to make the coefficients equal.

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What does it indicate if two lines are parallel when solving a system of equations?

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If two lines are parallel, it indicates that there is no solution to the system of equations, as they do not intersect.

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How can you check your solution after using the elimination method?

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You can check your solution by substituting the values back into the original equations to see if they hold true.

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What is the result of the elimination method if the two equations are identical?

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If the two equations are identical, it indicates that there are infinitely many solutions.