Problem Solving: Systems of Linear Inequalities

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Mathematics
•
9th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
What is a system of linear inequalities?
Back
A system of linear inequalities is a set of two or more linear inequalities that involve 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 represent a budget constraint in a linear inequality?
Back
A budget constraint can be represented as an inequality where the total cost of items does not exceed the budget. For example, if x is the number of item A and y is the number of item B, the inequality can be written as: cost_A * x + cost_B * y <= budget.
3.
FLASHCARD QUESTION
Front
What does the symbol '≥' represent in inequalities?
Back
The symbol '≥' means 'greater than or equal to'. It indicates that the value on the left side of the inequality is either greater than or equal to the value on the right side.
4.
FLASHCARD QUESTION
Front
What does the symbol '≤' represent in inequalities?
Back
The symbol '≤' means 'less than or equal to'. It indicates that the value on the left side of the inequality is either less than or equal to the value on the right side.
5.
FLASHCARD QUESTION
Front
How do you write an inequality for a minimum requirement?
Back
An inequality for a minimum requirement is written using the '≥' symbol. For example, if a minimum of 8 people is required, it can be expressed as: x + y ≥ 8.
6.
FLASHCARD QUESTION
Front
How do you write an inequality for a maximum capacity?
Back
An inequality for a maximum capacity is written using the '≤' symbol. For example, if the maximum capacity is 455 people, it can be expressed as: x ≤ 455.
7.
FLASHCARD QUESTION
Front
What is the first step in solving a system of linear inequalities?
Back
The first step in solving a system of linear inequalities is to graph each inequality on the same coordinate plane to find the feasible region where all inequalities overlap.
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