Qtr 2 checkpoint review #1

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What is a system of linear inequalities?

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A system of linear inequalities is a set of two or more inequalities with the same variables. The solution is the region where the graphs of the inequalities overlap.

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How do you represent a budget constraint in a linear inequality?

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This inequality represents a minimum requirement, indicating that the total number of items x and y must be at least 20.

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This inequality represents a budget constraint, indicating that the total cost of purchasing x small candles at $3.50 each and y large candles at $5.00 each cannot exceed $80.

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What is the significance of parallel lines in a system of equations?

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Parallel lines in a system of equations indicate that there is no solution, as the lines never intersect.

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What does it mean for a point to be a solution to a system of inequalities?

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A point is a solution to a system of inequalities if it satisfies all the inequalities in the system, meaning it lies in the overlapping region of the graphs.

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How can you determine if a point is a solution to a system of equations?

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To determine if a point is a solution, substitute the x and y values of the point into each equation. If the equations hold true, then the point is a solution.

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What is the graphical representation of a system of equations with no solution?

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The graphical representation of a system of equations with no solution consists of parallel lines that do not intersect.

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What does the term 'feasible region' refer to in linear programming?

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The feasible region is the area on a graph that satisfies all the constraints of a linear programming problem, representing all possible solutions.

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What is the purpose of using inequalities in real-world problems?

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Inequalities are used in real-world problems to represent constraints and limits, such as budgets, minimum requirements, and maximum capacities.