Final answer:
To represent meaningful answers in real-world situations using inequalities, include non-negativity constraints, and consider the limitations of the scenario being modeled, such as maximum capacities or budget constraints.
Step-by-step explanation:
When adding two inequalities to any system of inequalities, especially to represent meaningful answers to a real-world situation, you should consider constraints that apply to all scenarios. These typically include non-negativity constraints, where variables cannot be negative, because many real-world quantities (like distance, time, or number of items) cannot be less than zero.
For example, when working with systems of inequalities representing business operations, we could add x ≥ 0 and y ≥ 0 to ensure that the variables representing quantities, such as the number of products, would not be negative.
Working with systems of inequalities, it is also essential to realize that inequalities are tools to represent scenarios involving limited resources, maximum or minimum capacities, budget constraints, or scenarios where quantities are restricted within a certain range. In such cases, adding inequalities like x ≤ capacity or budget ≥ y is common to reflect these limitations.
These types of constraints help to model the real-world problem accurately and find a solution that is feasible in the given context.