Solving Linear-Quadratic Systems by Elimination

Solve using elimination:

Zen is a photographer and she is always on the hunt for the best views. One day she hears about a mountain that has one of the most beautiful views of the river and forest below. The problem is that it's almost impossible to get to the top of the mountain. The only way to get there is by hot air balloon. However there isn't a lot of landing room at the top of the mountain so the hot air balloon must land in a very specific place. The shape of the mountain side can be represented with the linear equation $y=x+\frac{7}{2}$. In order to land in the correct place the hot air balloon must follow the parabolic path represented by the quadratic equation $y-6=-\frac{1}{2}(x-3)^2$. What is the point that the hot air balloon must land at in order to safely get Zen to the top of the mountain?