Solve 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 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 the graphical method of solving systems of equations?

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Plotting the equations on a graph and identifying the point(s) where they intersect.

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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 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 represent a system of equations algebraically?

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Using two or more equations that relate the same variables, e.g., 2x + 3y = 6 and x - y = 2.

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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 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.