Systems of Equations Elimination (Easy)

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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 set of values that satisfy all equations simultaneously.

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What does it mean to solve a system of equations by elimination?

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Solving by elimination involves adding or subtracting equations to eliminate one variable, making it easier to solve for the remaining variable.

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What is the elimination method used for?

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The elimination method is used to find the values of variables in a system of equations by eliminating one variable at a time.

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

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If a system has no solution, it means the equations represent parallel lines that never intersect.

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

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If a system has infinitely many solutions, it means the equations represent the same line, and there are countless points of intersection.

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How do you determine if two equations are dependent?

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Two equations are dependent if they represent the same line, meaning one equation can be derived from the other by multiplication or division.

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What is the first step in solving a system of equations by elimination?

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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 facilitate elimination?

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You can multiply one or both equations by a constant to create coefficients that are opposites, allowing for easy elimination.

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What is the significance of the coefficients in a system of equations?

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Coefficients determine the slope and position of the lines represented by the equations, affecting their intersection.

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What is a consistent system of equations?

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A consistent system has at least one solution, meaning the lines intersect at one point or are the same line.