Systems of Inequalities review

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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 (for ≤ or ≥) or a dashed line (for < or >). Then, shade the region that satisfies the inequality.

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What does it mean when 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 happens to the inequality symbol when you multiply or divide by a negative number?

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The inequality symbol flips direction when you multiply or divide both sides of an inequality by a negative number.

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How do you determine if a point is a solution to an inequality?

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To determine if a point is a solution to an inequality, substitute the x and y values of the point into the inequality. If the inequality holds true, the point is a solution.

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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 find the intersection of two inequalities?

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

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What does it mean for a point to be 'not a solution' to a system of inequalities?

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A point is 'not a solution' if it does not satisfy at least one of the inequalities in the system, meaning it lies outside the shaded region.