Solving Systems of Equations

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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 elimination method?

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A technique for solving systems of equations by adding or subtracting equations to eliminate a variable.

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What is the substitution method?

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

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What is the graphing method?

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A method of solving systems 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 elimination method preferred?

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When the equations are in standard form and can be easily manipulated to eliminate a variable.

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When is the substitution method preferred?

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When one equation is already solved for one variable, making it easy to substitute into the other equation.

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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.