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 graphical representation of a system of equations?

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The intersection points of the lines representing each equation on a graph.

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What is a solution to a system of equations?

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A pair of values (x, y) that makes all equations in the system true.

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What is the substitution method 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 the elimination method 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 infinitely many 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 check if your solution to a system of equations is correct?

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Substitute the values of the variables back into the original equations to see if they hold true.

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What is a linear equation?

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An equation that forms a straight line when graphed, typically in the form y = mx + b.