System of Inequalities: Solution or Not a Solution?

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What is a system of inequalities?

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A system of inequalities is a set of two or more inequalities with 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 inequalities?

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

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What does it mean for a point to be a solution to an inequality?

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A point is a solution to an inequality if it makes the inequality true when the coordinates of the point are substituted into the inequality.

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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 is solid if the inequality is inclusive (≥ or ≤) and dashed if it is exclusive (> or <).

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What is the difference between a solid line and a dashed line in graphing inequalities?

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

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How do you graph the inequality y ≤ -2x + 5?

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To graph y ≤ -2x + 5, first graph the line y = -2x + 5 as a solid line. Then shade below the line to represent all points where y is less than or equal to -2x + 5.

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What does the solution set of a system of inequalities look like?

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The solution set of a system of inequalities is the region where the shaded areas of all inequalities overlap on the graph.

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What is the significance of the intersection of two inequalities?

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The intersection of two inequalities represents the set of points that satisfy both inequalities simultaneously, which is the solution to the system.

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How can you check if a point is not a solution to a system of inequalities?

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To check if a point is not a solution, substitute the point's coordinates into the inequalities. If it fails to satisfy any inequality, it is not a solution.

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What is the meaning of the term 'feasible region' in the context of inequalities?

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The feasible region is the area on a graph that represents all possible solutions to a system of inequalities.