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 graphing method most useful?

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When the equations are simple and can be easily graphed, or when a visual representation is needed.

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When is the substitution method most useful?

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When one equation is easily solvable for one variable, making substitution straightforward.

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When is the elimination method most useful?

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When the coefficients of one variable are easily manipulated to eliminate that variable.

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What does it mean if a system of equations has one solution?

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The lines representing the equations intersect at exactly one point.

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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.