FALL 2024 Semester Review - Updated

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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 large candles and small candles in a system of equations?

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Let x be the price of a large candle and y be the price of a small candle. The equations can be formed based on the total cost of candles sold.

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This equation represents the total cost of 3 large candles and 4 small candles, which equals $64.

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This equation represents the total cost of 1 large candle and 8 small candles, which equals $68.

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What is the first step in solving a system of equations?

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The first step is to express one variable in terms of the other using one of the equations.

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What is the significance of the slope in a linear equation?

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The slope indicates the rate of change of the dependent variable with respect to the independent variable.

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How do you interpret a negative rate of change?

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A negative rate of change indicates that as one variable increases, the other variable decreases.

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What is an inequality in mathematics?

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An inequality is a mathematical statement that compares two expressions and shows that one is greater than, less than, or not equal to the other.

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First, distribute and simplify both sides, then isolate x to find the solution set.

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This equation represents a straight line with a slope of 1/2, indicating that for every 2 units increase in x, y increases by 1 unit.