Solving Systems of Inequalities - 2024

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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 region where the graphs of the inequalities overlap.

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How do you graph a linear inequality?

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To graph a linear inequality, first graph the corresponding equation as a 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 to a system of inequalities represent?

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The solution to a system of inequalities represents all the points (x, y) that satisfy all inequalities in the system.

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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 significance of the shaded region in the graph of a system of inequalities?

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The shaded region represents all possible solutions to the system of inequalities. Any point within this region satisfies all inequalities.

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How do you find the intersection of two inequalities?

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To find the intersection, graph both inequalities and identify the region where their shaded areas overlap.

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What is a feasible region in the context of linear inequalities?

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A feasible region is the area on a graph where all constraints (inequalities) are satisfied, representing all possible solutions.