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 for an ordered pair to be a solution of a system of equations?

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It means that the ordered pair satisfies all equations in the system when substituted for the variables.

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How can you represent a real-world situation using a system of equations?

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By defining variables for the quantities involved and creating equations based on relationships and constraints.

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What is the graphical representation of a system of equations?

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The graphs of the equations plotted on the same coordinate plane, where the intersection points represent the solutions.

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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 two lines are parallel in the context of a system of equations?

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It means that the system has no solution, as the lines never intersect.

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What does it mean if two lines coincide in the context of a system of equations?

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It means that the system has infinitely many solutions, as every point on the line is a solution.

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How do you determine if a solution is valid for a system of equations?

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By substituting the solution into each equation and checking if the equations hold true.

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What is the significance of the coefficients in a system of equations?

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They represent the rate of change or the relationship between the variables in the equations.