Systems 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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What does it mean for a point to be a solution to a system of linear inequalities?

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A point is a solution to a system of linear inequalities if it satisfies all inequalities in the system, meaning it lies in the region defined by the inequalities.

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What is the difference between a solid line and a dotted line when graphing inequalities?

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

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What is the significance of the boundary line in a system of linear inequalities?

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The boundary line separates the coordinate plane into two regions: one that satisfies the inequality and one that does not. Solutions to the inequality are found in the shaded region.

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

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A system of inequalities has no solution if the shaded regions of the inequalities do not overlap, meaning there are no points that satisfy all inequalities.

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How can you tell if a graph represents a system of inequalities?

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A graph represents a system of inequalities if it shows multiple shaded regions corresponding to different inequalities, with the overlapping area indicating the solution set.