What is a system of inequalities?
Solving Systems of Inequalities

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Mathematics
•
9th 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 points that satisfy all inequalities in the system.
2.
FLASHCARD QUESTION
Front
How do you graph a linear inequality?
Back
To graph a linear inequality, first graph the corresponding equation as a line. Use a solid line for ≤ or ≥ and a dashed line for < or >. Then shade the region that satisfies the inequality.
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 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 (≤ or ≥), while a dashed line indicates that points on the line are not included ( < or >).
5.
FLASHCARD QUESTION
Front
What is the solution set of a system of inequalities?
Back
The solution set is the collection of all points that satisfy all inequalities in the system, often represented as a shaded region on a graph.
6.
FLASHCARD QUESTION
Front
How can you determine if a point is a solution to a system of inequalities?
Back
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.
7.
FLASHCARD QUESTION
Front
What does it mean if a system of inequalities has no solution?
Back
A system of inequalities has no solution if the shaded regions of the inequalities do not overlap, meaning there are no points that satisfy all inequalities.
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