Solve 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.

Tags

CCSS.HSA.REI.D.12

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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. Then, shade the region that satisfies the inequality (above the line for 'greater than' and below for 'less than').

Tags

CCSS.HSA.REI.D.12

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What does it mean if a line is dashed in a graph of an inequality?

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

Tags

CCSS.HSA.REI.D.12

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What does it mean if a line is solid in a graph of an inequality?

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

Tags

CCSS.HSA.REI.D.12

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What is the solution to the system of inequalities y > -x - 1 and y ≥ x + 4?

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The solution is the region where the graphs of both inequalities overlap.

Tags

CCSS.HSA.REI.D.12

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

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What is the significance of the feasible region in a system of inequalities?

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The feasible region is the area on the graph where all the inequalities overlap, representing all possible solutions to the system.

Tags

CCSS.HSA.REI.D.12

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How can you represent a real-world situation using a system of inequalities?

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You can represent constraints and objectives in a real-world situation (like time, cost, or resources) using inequalities to model the relationships.

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What is the first step in solving a system of inequalities by graphing?

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The first step is to graph each inequality on the same coordinate plane.

Tags

CCSS.HSA.REI.D.12

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What does the inequality s + t ≤ 20 represent in a real-world context?

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It represents a constraint where the total hours worked (s for tutoring and t for pet sitting) cannot exceed 20 hours.