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

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

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To determine if a point is a solution, 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 point is not a solution to a system of linear inequalities?

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If a point is not a solution, it means that when the coordinates are substituted into the inequalities, at least one inequality is not satisfied.

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What is the graphical representation of a linear inequality?

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The graphical representation of a linear inequality is a half-plane divided by a line. The line represents the boundary, and the half-plane indicates the region where the inequality holds true.

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What is the difference between a solid line and a dashed line in the graph of linear inequalities?

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A solid line indicates that the points on the line are included in the solution (≤ or ≥), while a dashed line indicates that the points on the line are not included ( < or >).

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How can you find the solution set of a system of linear inequalities graphically?

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To find the solution set graphically, graph each inequality on the same coordinate plane and identify the region where the shaded areas overlap. This overlapping region represents the solution set.

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

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The feasible region is the area on the graph that satisfies all inequalities in the system. It is the intersection of all the half-planes.

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What is an example of a linear inequality?

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An example of a linear inequality is y < 2x + 3.

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How do you write a system of linear inequalities from a word problem?

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To write a system of linear inequalities from a word problem, identify the variables, translate the conditions into inequalities, and express them as a system.

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What is the significance of the solution to a system of linear inequalities in real-world applications?

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The solution to a system of linear inequalities can represent constraints in real-world scenarios, such as budget limits, resource allocations, or production capacities.