1. **State the problem:** We need to find values of $x$ and $y$ that satisfy the system of equations: $$3x + y = 25$$ $$xy = 0$$ 2. **Understand the second equation:** The product $xy = 0$ means either $x = 0$ or $y = 0$ (or both). 3. **Case 1: $x = 0$** Substitute $x = 0$ into the first equation: $$3(0) + y = 25$$ $$y = 25$$ So one solution is $(x, y) = (0, 25)$. 4. **Case 2: $y = 0$** Substitute $y = 0$ into the first equation: $$3x + 0 = 25$$ $$3x = 25$$ Divide both sides by 3: $$\cancel{3}x = \frac{25}{\cancel{3}}$$ $$x = \frac{25}{3}$$ So the other solution is $(x, y) = \left(\frac{25}{3}, 0\right)$. 5. **Final answer:** The solutions to the system are: $$\boxed{(0, 25) \text{ and } \left(\frac{25}{3}, 0\right)}$$