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 cost of items in a system of equations?

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

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

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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. It shows how much y changes for a unit change in x.

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This equation represents a line with a slope of -1/3 and a y-intercept of 2, indicating that for every 3 units you move right, the line moves down 1 unit.

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How do you determine the rate of change from a graph?

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The rate of change can be determined by calculating the slope of the line, which is the rise over run (change in y over change in x).

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What is the meaning of an inequality in a graph?

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An inequality represents a range of values rather than a single value, indicating that the solution set includes all points that satisfy the inequality.

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How do you solve a system of equations using substitution?

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To solve using substitution, solve one equation for one variable and substitute that expression into the other equation to find the values of both variables.

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What is the purpose of using variables in equations?

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Variables are used to represent unknown quantities in equations, allowing us to formulate relationships and solve for those unknowns.