Graphing 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 that share the same variables. The solution is the set of all points that satisfy all inequalities in the system.

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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 the inequalities in the system, meaning it lies in the overlapping shaded region when graphed.

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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 is the difference between a dashed line and a solid line in graphing inequalities?

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A dashed line indicates that points on the line are not included in the solution (for < or >), while a solid line indicates that points on the line are included (for ≤ or ≥).

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What does the term 'overlap' refer to in the context of graphing systems of inequalities?

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'Overlap' refers to the region where the shaded areas of two or more inequalities intersect, representing the set of solutions that satisfy all inequalities.

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How can you determine if a point is in the solution set of a system of inequalities?

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To determine if a point is in the solution set, substitute the coordinates of the point into each inequality. If the point satisfies all inequalities, it is part of the solution set.

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What is the significance of the solution set in a system of inequalities?

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The solution set represents all possible solutions that satisfy the conditions of the inequalities, often visualized as a shaded region on a graph.

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What is an ordered pair?

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An ordered pair is a pair of numbers used to represent a point in a coordinate system, typically written in the form (x, y).

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What does it mean for a point to NOT be part of the solution set?

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A point is NOT part of the solution set if it does not satisfy at least one of the inequalities in the system, meaning it lies outside the shaded region.

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How do you identify a solution from a set of ordered pairs?

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To identify a solution from a set of ordered pairs, substitute each pair into the inequalities. The pairs that satisfy all inequalities are the solutions.