Systems of Equations: Choosing the Best Method

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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 a system of equations by solving one equation for one variable and substituting that expression into the other equation.

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What is the elimination method?

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

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What is the graphing method?

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A method for solving a system of equations by graphing the equations on the same coordinate plane and identifying the point(s) of intersection.

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When is the substitution method most useful?

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When one equation is already solved for one variable or can be easily manipulated to do so.

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When is the elimination method most useful?

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When the coefficients of one variable are the same or can be easily made the same.

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When is the graphing method most useful?

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When you want a visual representation of the solution or when the equations are simple enough to graph easily.

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What is the solution to a system of equations?

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The point(s) where the graphs of the equations intersect, representing the values of the variables that satisfy all equations.

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

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The lines representing the equations are parallel and never intersect.