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 solid line (if the inequality is ≤ or ≥) or a dashed line (if it is < or >). Then, shade the region that satisfies the inequality.

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What does it mean if a point is 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 inequalities in the system, meaning it lies in the shaded region of the graph.

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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 (for ≤ or ≥), while a dashed line indicates that points on the line are not included (for < or >).

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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 coordinates of the point into each inequality. If the point satisfies all inequalities, it is a solution.

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What does the solution set of a system of inequalities look like?

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The solution set of a system of inequalities is the overlapping shaded region of the graphs of the individual inequalities.

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How do you find the intersection of two inequalities?

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To find the intersection, graph both inequalities and identify the region where the shaded areas overlap. This overlapping region represents the solution set.

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What is the significance of the boundary line in a linear inequality?

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The boundary line separates the graph into two regions: one that satisfies the inequality and one that does not. It helps determine where to shade.

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What does the inequality @@y eq 3@@ represent graphically?

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