Systems of Equations Elimination Easy Type

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What is a system of equations?

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A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

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What is the elimination method in solving systems of equations?

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The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other variable.

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

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A system has one solution if the lines intersect at one point, no solution if the lines are parallel, and infinitely many solutions if the lines are the same.

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What does it mean for two equations to be dependent?

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Two equations are dependent if they represent the same line, meaning they have infinitely many solutions.

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What does it mean for two equations to be independent?

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Two equations are independent if they represent different lines that intersect at exactly one point, meaning they have a unique solution.

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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 so that corresponding variables and constants are in the same columns.

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How can you manipulate equations to use the elimination method?

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You can multiply one or both equations by a constant to create coefficients that will allow for the elimination of one variable.

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What is the significance of the ordered pair in the context of systems of equations?

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The ordered pair represents the solution to the system, indicating the values of the variables that satisfy both equations.

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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 align the equations or miscalculating when adding or subtracting the equations.

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How do you check your solution after solving a system of equations?

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You can check your solution by substituting the ordered pair back into the original equations to see if both equations are satisfied.