FALL 2024 Semester Review

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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 simultaneously.

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How do you represent the price of items in a system of equations?

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You can represent the price of items using variables, such as x for the price of a large candle and y for the price of a small candle, and create equations based on given information.

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This equation represents the total cost of 3 large candles (x) and 4 small candles (y) equaling $64.

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What is the purpose of solving a system of equations?

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The purpose is to find the values of the variables that make all equations true, often representing real-world quantities.

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This equation signifies that the total cost of 1 large candle (x) and 8 small candles (y) is $68.

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How can you determine the price of tickets using a system of equations?

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By setting up equations based on the total sales from different combinations of adult and child tickets.

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

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Coefficients represent the quantity of each variable in the context of the problem, such as the number of tickets sold.

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This equation represents a linear relationship between x and y, indicating how y changes with respect to x.

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How do you find the cost of one item when given total costs and quantities?

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You can set up a system of equations based on the total costs and quantities, then solve for the price of one item.

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This equation shows the total revenue from selling 5 adult tickets (a) and 2 child tickets (c) equals $70.