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 share 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 dashed or solid line (depending on whether the inequality is strict or inclusive). 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 strict and non-strict inequality?

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A strict inequality (e.g., < or >) does not include the boundary line, while a non-strict inequality (e.g., ≤ or ≥) includes the boundary line.

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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, where any point within this region satisfies all inequalities.

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What does the intersection of two inequalities represent?

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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 in 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 linear inequalities?

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A boundary line is the line that represents the equation of the inequality. It divides the graph into two regions: one that satisfies the inequality and one that does not.

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What is the role of test points in solving systems of inequalities?

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Test points are used to determine which side of the boundary line satisfies the inequality. By testing a point, you can identify the correct shaded region.