Setting Up Word Problems Systems

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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 is the set of values that satisfy all equations in the system.

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How do you represent a word problem as a system of equations?

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Identify the variables, write equations based on the relationships described in the problem, and ensure the equations reflect the conditions given.

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What does the variable 'x' typically represent in a word problem?

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'x' usually represents the quantity of one type of item or variable in the context of the problem.

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What does the variable 'y' typically represent in a word problem?

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'y' usually represents the quantity of another type of item or variable in the context of the problem.

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How do you determine the total cost in a word problem involving prices?

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Multiply the quantity of each item by its price and sum the results to find the total cost.

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

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Coefficients represent the rate or quantity of each variable in the equations, indicating how much each variable contributes to the total.

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What does it mean if two equations in a system are dependent?

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Dependent equations have infinitely many solutions, as they represent the same line or relationship in a graph.

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What does it mean if two equations in a system are independent?

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Independent equations have a unique solution, as they represent different lines that intersect at one point.

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What does it mean if two equations in a system are inconsistent?

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Inconsistent equations have no solution, as they represent parallel lines that never intersect.

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How can 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 satisfy all equations.