EOC Boot Camp Systems of Linear Inequalities

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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 that involve the same variables. The solution to the system is the set of all points that satisfy all inequalities in the system.

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

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To determine if a point is a solution to a system of inequalities, substitute the coordinates of the point into each inequality. If the point satisfies all inequalities, it is a solution.

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What does it mean if a system of linear inequalities has no solution?

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A system of linear inequalities has no solution if the graphs of the inequalities do not overlap, meaning there are no points that satisfy all inequalities simultaneously.

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What is the significance of boundary lines in a system of inequalities?

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Boundary lines represent the limits of the inequalities. The area above or below the line (depending on the inequality) indicates the region where solutions exist.

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What does it mean for boundary lines to be parallel in a system of inequalities?

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If the boundary lines of a system of inequalities are parallel, it indicates that the inequalities do not intersect, leading to no solution for the system.

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How do you graph a linear inequality?

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To graph a linear inequality, first graph the corresponding linear equation as a solid line (for ≤ or ≥) or a dashed line (for < or >). Then shade the region that satisfies the inequality.

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What is the role of the feasible region in a system of inequalities?

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The feasible region is the area on the graph where all the inequalities overlap. It represents all possible solutions to the system.

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How do you find the vertices of the feasible region?

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To find the vertices of the feasible region, identify the points where the boundary lines intersect, as these points are potential solutions to the system.

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What is the objective function in a linear programming problem?

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The objective function is a mathematical expression that defines the goal of the problem, typically to maximize or minimize a certain quantity, such as profit or cost.

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How do you convert a word problem into a system of inequalities?

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To convert a word problem into a system of inequalities, identify the variables, constraints, and objective, then express the relationships using inequalities.