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.

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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.

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What is substitution in solving systems of equations?

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

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What is elimination in solving systems of equations?

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A method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.

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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.

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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 infinite solutions?

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

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How do you graph a system of equations?

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Graph each equation on the same coordinate plane and look for points of intersection.

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What is the first step in solving a system of equations by substitution?

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Solve one of the equations for one variable in terms of the other.

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What is the first step in solving a system of equations by elimination?

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Align the equations and manipulate them to eliminate one variable.