Graphing Systems of Linear Inequalities
Flashcard
•
Mathematics
•
8th - 9th Grade
•
Practice Problem
•
Hard
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15 questions
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1.
FLASHCARD QUESTION
Front
What is a linear inequality?
Back
A linear inequality is a mathematical statement that compares a linear expression to a value using inequality symbols (>, <, ≥, ≤).
2.
FLASHCARD QUESTION
Front
How do you graph a linear inequality?
Back
To graph a linear inequality, first graph the corresponding linear equation as a dashed (for < or >) or solid 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 linear inequality?
Back
A point is a solution to a linear inequality if it lies in the shaded region of the graph, meaning it satisfies the inequality.
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
How can you determine if a point is a solution to a system of linear inequalities?
Back
Substitute the coordinates of the point into each inequality. If the point satisfies all inequalities, it is a solution to the system.
6.
FLASHCARD QUESTION
Front
What is the solution set of a system of linear inequalities?
Back
The solution set is the region on the graph where the shaded areas of all inequalities overlap.
7.
FLASHCARD QUESTION
Front
What does it mean for a system of linear inequalities to be inconsistent?
Back
A system of linear inequalities is inconsistent if there is no point that satisfies all inequalities, meaning the shaded regions do not overlap.
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