What is a system of linear inequalities?
Systems of Linear Inequalities

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•
Mathematics
•
8th - 9th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
Back
A system of linear inequalities is a set of two or more linear inequalities that share 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 system of linear inequalities?
Back
To graph a system of linear inequalities, first graph each inequality as if it were an equation. Use a dashed line for inequalities that do not include equality (e.g., < or >) and a solid line for those that do (e.g., ≤ or ≥). Then, shade the appropriate region for each inequality, and the solution is where the shaded regions overlap.
3.
FLASHCARD QUESTION
Front
What does the solution to a system of linear inequalities represent?
Back
The solution to a system of linear inequalities represents all the points (x, y) that satisfy all the inequalities in the system, typically visualized as a shaded region on a 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 the points on the line are included in the solution (≤ or ≥), while a dashed line indicates that the points on the line are not included ( < or >).
5.
FLASHCARD QUESTION
Front
What is the significance of the intersection of shaded regions in a graph of inequalities?
Back
The intersection of shaded regions in a graph of inequalities represents the set of solutions that satisfy all inequalities in the system.
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 x and y values of the point into each inequality. If the point satisfies all inequalities, it is a solution.
7.
FLASHCARD QUESTION
Front
What is the graphical representation of the inequality y < 2x - 1?
Back
The graphical representation is a dashed line for the equation y = 2x - 1, with the area below the line shaded.
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