Task #3: System of Linear Inequalities Graphs

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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 boundary line. Use a dashed line for inequalities that do not include equality (e.g., < or >) and a solid line for those that do (e.g., ≤ 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 points on the line are included in the solution (for ≤ or ≥), while a dashed line indicates that points on the line are not included (for < or >).

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How can you determine if a point is a solution to a linear inequality?

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To determine if a point is a solution, substitute the x and y values of the point into the inequality. If the inequality holds true, then the point is a solution.

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

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The solution set is represented by the overlapping shaded regions of the inequalities on the graph, indicating all points that satisfy all inequalities.

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What is the significance of the intersection of shaded regions in a graph of inequalities?

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The intersection of shaded regions represents the set of solutions that satisfy all inequalities in the system.

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How do you identify a solution from a list of points?

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Substitute each point into the inequalities of the system. The point that satisfies all inequalities is the solution.

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