System of Inequalities Review

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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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What does a dashed line represent in graphing inequalities?

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A dashed line indicates that the points on the line are not included in the solution set (i.e., the inequality is strict, using < or >).

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What does a solid line represent in graphing inequalities?

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A solid line indicates that the points on the line are included in the solution set (i.e., the inequality is non-strict, using ≤ or ≥).

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How do you determine if a point is a solution to a system of inequalities?

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Substitute the coordinates of the point into each inequality. If the point satisfies all inequalities, it is a solution.

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What is the difference between strict and non-strict inequalities?

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Strict inequalities (<, >) do not include the boundary line, while non-strict inequalities (≤, ≥) do include the boundary line.

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

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The solution set is typically a shaded region on the graph where all inequalities overlap.

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What is the significance of the intersection of two inequalities?

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The intersection represents the set of points that satisfy both inequalities simultaneously.

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How do you identify the correct system of inequalities from a graph?

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Analyze the slopes and y-intercepts of the lines, and determine whether they are solid or dashed to match the inequalities.