Systems of Inequalities

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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 system of inequalities?

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To graph a system of inequalities, first graph each inequality as if it were an equation. 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 it mean for a point to be a solution to a system of inequalities?

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A point is a solution to a system of inequalities if it satisfies all inequalities in the system, meaning it lies in the shaded region of the 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 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 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 x and y values of the point into each inequality. If the point satisfies all inequalities, it is a solution.

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What does the inequality y < 2x - 4 represent graphically?

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The inequality y < 2x - 4 represents the region below the line y = 2x - 4, where all points (x, y) satisfy the inequality.

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What is the solution set of a system of inequalities?

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The solution set of a system of inequalities is the set of all points that satisfy all inequalities in the system, represented graphically as the overlapping shaded regions.

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What does it mean if a point is not part of the solution set?

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If a point is not part of the solution set, it means that it does not satisfy at least one of the inequalities in the system.

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How do you identify the feasible region in a system of inequalities?

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The feasible region is identified by finding the overlapping area of the shaded regions of all inequalities in the system.

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

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Boundary lines separate the solution set from the non-solution set. They help determine where the inequalities hold true.