What is a system of inequalities?
Systems of Inequalities

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Mathematics
•
8th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
Back
A system of inequalities is a set of two or more inequalities with the same variables. The solution is the set of all ordered pairs that satisfy all inequalities in the system.
2.
FLASHCARD QUESTION
Front
How do you graph a system of inequalities?
Back
To graph a system of inequalities, first graph each inequality on the same coordinate plane. Use a solid line for '≤' or '≥' and a dashed line for '<' or '>'. The solution set is the region where the shaded areas overlap.
3.
FLASHCARD QUESTION
Front
What does it mean for a point to be a solution to a system of inequalities?
Back
A point is a solution to a system of inequalities if it satisfies all inequalities in the system, meaning it lies in the overlapping shaded region of the graph.
4.
FLASHCARD QUESTION
Front
What is the difference between a solid line and a dashed line in graphing inequalities?
Back
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 '>').
5.
FLASHCARD QUESTION
Front
How can you determine if a point is part of the solution set for a system of inequalities?
Back
To determine if a point is part of the solution set, substitute the coordinates of the point into each inequality. If the point satisfies all inequalities, it is part of the solution set.
6.
FLASHCARD QUESTION
Front
What is the solution set of the inequalities y < 2x + 3 and y ≥ -x - 1?
Back
The solution set is the region where the area below the line y = 2x + 3 and above the line y = -x - 1 overlap.
7.
FLASHCARD QUESTION
Front
What does the term 'feasible region' refer to in the context of systems of inequalities?
Back
The feasible region is the area on the graph that represents all possible solutions to the system of inequalities.
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