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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CCSS.8.EE.C.8B

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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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CCSS.HSA.REI.D.12

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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 >).

Tags

CCSS.HSA.REI.D.12

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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.

Tags

CCSS.HSA.REI.D.12

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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.

Tags

CCSS.HSA.REI.D.12

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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.