Maximizing Cupcakes in Bakery Production

A small bakery produces cupcakes and cookies. The bakery can make a maximum of 200 items per day. Each cupcake takes 2 hours to make, while each cookie requires 1 hour. The bakery owner has a total of 12 hours available for baking each day.

Let $x$ be the number of cupcakes made and $y$ be the number of cookies made. Based on these conditions, write and solve a system of linear equations to determine the possible combinations of cupcakes and cookies that can be produced in one day without exceeding the item and time constraints. Calculate the value of $y$ when the bakery produces the maximum number of cupcakes ($x$).