Step 1 :Define two variables: let x be the number of gifts Jackson wrapped and y be the number of gift bags he prepared.
Step 2 :From the problem, we know that the total number of gifts is 25. This gives us the equation \(x + y = 25\).
Step 3 :We also know that Jackson spent 110 minutes preparing the gifts, and since he spends 6 minutes per wrapped gift and 2 minutes per gift bag, we have the equation \(6x + 2y = 110\).
Step 4 :So, the system of equations is: \(x + y = 25\) and \(6x + 2y = 110\).
Step 5 :Final Answer: The system of equations is \(\boxed{x + y = 25}\) and \(\boxed{6x + 2y = 110}\), where x is the number of gifts Jackson wrapped and y is the number of gift bags he prepared.