6.1 - 6.2 Solutions to Systems of Inequalities Practice

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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 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 does the symbol '≥' mean in an inequality?

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'≥' means 'greater than or equal to'. It indicates that the value can be either greater than or equal to a certain number.

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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 can be either less than or equal to a certain number.

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What is the solution set of a system of inequalities?

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The solution set is the region on the graph where the shaded areas of all inequalities overlap. It represents all possible solutions that satisfy all inequalities.

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

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A dashed line indicates that the points on the line are not included in the solution (strict inequality), while a solid line indicates that the points on the line are included (inclusive inequality).

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What is the significance of the intersection of two inequalities?

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

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How do you solve a system of inequalities graphically?

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To solve graphically, graph each inequality on the same coordinate plane and identify the overlapping shaded region, which represents the solution set.