Systems of Equations: Choosing the Best Method

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What is a system of equations?

Back

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?

Back

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

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What is the substitution method?

Back

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 the graphing method?

Back

A method for solving systems of equations by graphing each equation on the same set of axes 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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What is a solution to a system of equations?

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A set of values for the variables that makes all equations in the system true.

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

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The lines represented by the equations are parallel and never intersect.

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

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The equations represent the same line, meaning every point on the line is a solution.