1. **State the problem:** We need to write a system of equations to find the weight of each large box ($x$) and each small box ($y$) based on the given deliveries. 2. **Define variables:** Let $x$ be the weight of each large box in kilograms. Let $y$ be the weight of each small box in kilograms. 3. **Form equations from the data:** - First delivery: 5 large boxes and 3 small boxes weigh 131 kg total. - Second delivery: 2 large boxes and 6 small boxes weigh 116 kg total. 4. **Write the system of equations:** $$5x + 3y = 131$$ $$2x + 6y = 116$$ This system can be solved to find $x$ and $y$. 5. **Summary:** The system of equations is: $$5x + 3y = 131$$ $$2x + 6y = 116$$