Graphing Systems of Linear Inequalities

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What is a linear inequality?

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A linear inequality is a mathematical statement that relates a linear expression to a value using inequality symbols (>, <, ≥, ≤). It represents a region of the coordinate plane.

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What does the solution set of a system of linear inequalities represent?

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The solution set represents all the points that satisfy all inequalities in the system, typically shown as a shaded region on a graph.

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How do you graph a linear inequality?

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1. Graph the corresponding linear equation as a boundary line. 2. Use a dashed line for < or > and a solid line for ≤ or ≥. 3. Shade the region that satisfies the inequality.

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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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What does it mean if a system of inequalities has no solution?

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It means that there is no point that satisfies all inequalities in the system, often represented by parallel lines that never intersect.

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What does it mean if a system of inequalities has an infinite number of solutions?

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It means that there are infinitely many points that satisfy all inequalities, often represented by overlapping shaded regions.

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How can you determine if a point is part of the solution set for 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 part of the solution set.

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What is the significance of the intersection of two inequalities in a system?

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The intersection represents the set of points that satisfy both inequalities, which is the solution set for the system.

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How do you solve a system of inequalities by graphing?

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1. Graph each inequality on the same coordinate plane. 2. Identify the overlapping shaded region. 3. This region represents the solution set.