The graph represents a system of inequalities for the scenario where x is the number of confirmed parties on a tour and y is the number of required copies of the itinerary. Which constraint could be part of this system of equations?
At least 2 copies are required per tour.
More than 2 copies are required per tour.
The number of confirmed parties must be at least double the number of required copies.
The number of confirmed parties must be no more than double the number of required copies.
At least 2 copies are required per tour
To determine which constraint could be part of the system of inequalities, we need to analyze the information provided and understand how it can be represented on a graph.
Let's focus on the two variables, x (number of confirmed parties on a tour) and y (number of required copies of the itinerary).
1. "At least 2 copies are required per tour":
This means that the minimum number of required copies is 2. In terms of the graph, it implies that the line representing this constraint should pass through the points where the y-value is equal to 2 or higher. Therefore, the line would be represented as y ≥ 2.
2. "More than 2 copies are required per tour":
This statement means that the number of required copies is greater than 2. Likewise, the line representing this constraint should pass through the points where the y-value is greater than 2. It would be represented as y > 2.
3. "The number of confirmed parties must be at least double the number of required copies":
This constraint suggests that the number of confirmed parties should be equal to or greater than twice the number of required copies. In terms of the graph, it would be represented as x ≥ 2y.
4. "The number of confirmed parties must be no more than double the number of required copies":
This condition states that the number of confirmed parties should be less than or equal to twice the number of required copies. On the graph, it would be represented as x ≤ 2y.
Considering the options provided, the most appropriate constraint that could be part of the system of equations is therefore:
"The number of confirmed parties must be at least double the number of required copies" (represented as x ≥ 2y).