Solving Systems of Equations Final

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What is a system of equations?

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A set of two or more equations with the same variables that are solved together.

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What does it mean to solve a system of equations?

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Finding the values of the variables that satisfy all equations in the system simultaneously.

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What is the substitution method?

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A method for solving systems of equations where one equation is solved for one variable, and that expression is substituted into the other equation.

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What is the elimination method?

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A method for solving systems of equations by adding or subtracting equations to eliminate one variable.

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What is graphing in the context of systems of equations?

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A method of solving systems by plotting the equations on a graph and identifying the point(s) where they intersect.

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What is an ordered pair?

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A pair of numbers (x, y) that represent a point in a two-dimensional space.

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What does it mean if two lines intersect at a point?

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The point of intersection represents the solution to the system of equations.

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What is a consistent system of equations?

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A system that has at least one solution.

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What is an inconsistent system of equations?

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A system that has no solutions.

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What is a dependent system of equations?

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A system that has infinitely many solutions, where the equations represent the same line.