Systems of Equations Process Questions

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What is a system of equations?

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A system of equations is a set of two or more equations with the same variables. The solution to the system is the set of values that satisfy all equations simultaneously.

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What does it mean if two lines in a system of equations are graphed on top of each other?

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If two lines in a system of equations are graphed on top of each other, it means that the equations represent the same line, resulting in infinitely many solutions.

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What is the solution to a system of equations with no points of intersection?

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The solution to a system of equations with no points of intersection is 'No Solution', indicating that the lines are parallel.

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What is the elimination method in solving systems of equations?

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The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the remaining variable.

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How can you determine if a system of equations has a unique solution?

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A system of equations has a unique solution if the lines intersect at exactly one point, meaning the equations are not parallel and not the same line.

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What does it mean for two equations to be dependent?

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Two equations are dependent if they represent the same line, resulting in infinitely many solutions.

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What is the graphical representation of a system of equations?

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The graphical representation of a system of equations consists of the lines corresponding to each equation plotted on the same coordinate plane.

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What is the substitution method in solving systems of equations?

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The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

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What are opposite coefficients in the context of elimination?

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Opposite coefficients are values in front of the same variable in different equations that are equal in magnitude but opposite in sign, allowing for elimination when added.

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What is the significance of the point of intersection in a system of equations?

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The point of intersection represents the solution to the system of equations, indicating the values of the variables that satisfy all equations.