Dolora spends at least 4 hours per week gardening. She spends more time on routine maintenance such as weeding, pruning, and watering than on harvesting vegetables or flowers. She spends at least 1 hour per week harvesting. Which system of inequalities represents Dolora's weekly gardening time if x represents the number of weekly hours spent on routine garden maintenance and y represents the number of weekly hours spent on harvesting?

Since Dolora spends at least 4 hours per week gardening, this means that $x+y\ge4$. Additionally, since she spends more time on routine maintenance than on harvesting, this means that $x>y$. Thus, the system of inequalities that represents Dolora's weekly gardening time is: $\boxed{\begin{cases} x+y\ge4 \\ x>y \end{cases}}$.