Dec 06_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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How do you graph a linear inequality?

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To graph a linear inequality, first graph the corresponding linear equation as a boundary line. Then, shade the region that satisfies the inequality (above the line for 'greater than' and below for 'less than').

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

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'≤' means 'less than or equal to'. It indicates that the value on the left can be less than or equal to the value on the right.

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

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'≥' means 'greater than or equal to'. It indicates that the value on the left can be greater than or equal to the value on the right.

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What is the solution set of a system of inequalities?

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The solution set is the set of all ordered pairs (x, y) that satisfy all inequalities in the system.

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How can 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 x and y values of the point into each inequality. If the point satisfies all inequalities, it is part of the solution set.

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

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A system has no solution if there is no point that satisfies all inequalities simultaneously, often resulting in parallel lines that never intersect.

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

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A system has infinite solutions if the inequalities represent the same line or overlapping regions, meaning there are countless points that satisfy the system.

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How do you identify the feasible region in a system of inequalities?

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The feasible region is the area where the shaded regions of all inequalities overlap. It represents all possible solutions to the system.

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What is the significance of the boundary line in graphing inequalities?

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The boundary line separates the graph into two regions. Points on the line are included if the inequality is '≤' or '≥', and excluded if it is '<' or '>'.