Let's answer the question step by step: --- **Step 1: Understand what \(x\) and \(y\) represent in the system.** \(x\) and \(y\) are described as the populations of two species. In real life, population sizes cannot be negative; you can't have a negative number of individuals in a population. *Explanation:* Since \(x\) and \(y\) represent actual counts of living organisms, the smallest possible value for either is 0 (representing extinction or absence). Negative values would not make sense physically or biologically. --- **Step 2: Interpret why the conditions \(x \geq 0\) and \(y \geq 0\) are necessary.** The system models real populations, so it must reflect this reality in the mathematics. This means we should always restrict our attention to solutions where \(x \geq 0\) and \(y \geq 0\). *Explanation:* Allowing negative values would contradict the interpretation of \(x\) and \(y\) as populations. Therefore, it's natural and correct to require \(x \geq 0\) and \(y \geq 0\) in this model. --- **Final Answer:** It makes sense that \(x \geq 0\) and \(y \geq 0\) because \(x\) and \(y\) represent the populations of two species, and population sizes cannot be negative in reality.