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 with 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 when substituted into them.

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

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To determine if a point is a solution, 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 significance of boundary lines in systems of inequalities?

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Boundary lines represent the limits of the inequalities. They can be solid (inclusive) or dashed (exclusive) depending on whether the inequality includes equality.

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What does a dashed boundary line indicate?

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A dashed boundary line indicates that the points on the line are not included in the solution set (used for inequalities like < or >).

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What does a solid boundary line indicate?

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A solid boundary line indicates that the points on the line are included in the solution set (used for inequalities like ≤ or ≥).

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How do you graph a system of inequalities?

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To graph a system of inequalities, graph each inequality on the same coordinate plane, using solid or dashed lines as appropriate, and shade the region that satisfies each inequality.

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What is the solution region in a system of inequalities?

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The solution region is the area where the shaded regions of all inequalities overlap. This region contains all the points that satisfy the system.

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What does the symbol '≥' mean in an inequality?

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The symbol '≥' means 'greater than or equal to', indicating that the value can be either greater than or equal to the boundary.

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What does the symbol '>' mean in an inequality?

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The symbol '>' means 'greater than', indicating that the value must be strictly greater than the boundary.