Systems of Inequalities Practice

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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 graph a linear inequality?

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

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What does the solution set of a system of inequalities represent?

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The solution set represents all the points (x, y) that satisfy all inequalities in the system, often visualized as a shaded region on a graph.

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

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What is the graphical representation of the inequality @@y eq 2x + 3@@?

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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.

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How do you find the feasible region for a system of inequalities?

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The feasible region is found by graphing all inequalities and identifying the overlapping shaded area that satisfies all conditions.

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What is a boundary line in the context of inequalities?

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A boundary line is the line that represents the equation of the inequality. It divides the graph into regions that satisfy or do not satisfy the inequality.