Hail, GPS! Mystery Cache

As I mulled over various high-school-math-level ideas for a new puzzle cache, I had a "shower moment": instead of some random math problem, how 'bout one illustrating the problems our little GPS receivers solve to help us find geocaches?

The ingenious GPS system enables our devices to precisely (within ~10 feet) calculate our location and altitude from the signals of 4 or more GPS satellites. The devices calculate the distance to each satellite, which in 3-dimensional space defines a sphere of possible device locations relative to the satellite in the center. The 4 spheres are intersected using a method called trilateration, which yields the single location of the device in 3D space. There is of course a vast ocean more information than this mere drop about the history and details of GPS available on the web, so I encourage you to explore it if you're interested.

As you may have seen from the link above, actually performing trilateration on spheres involves some pretty advanced math, so to find this cache you'll instead solve the much simpler 2-D trilateration problem to at least get a taste of it. Here's the challenge: determine the (x, y) coordinates of the point at which the following 3 circles intersect:

While you can "cheat" by using online tools to solve the problem for you, I encourage you not to and instead to challenge yourself by solving it with paper and pencil. It's just basic high school algebra, so show yourself and your loved ones you can still do it! And be sure to call out your accomplishment in your log message.

The cache is located at N37 19.AB6, W122 07.CD8, where A=x*3 + 8, B=x+3, C=y+2, and D=y+9 and A-D are all modulo 10.

The cache is a camouflaged soda bottle preform a few feet off the trail. You'll need to bring your own pen for the log.

As you approach GZ with the help of your GPSr, I hope you'll appreciate a bit more the magic and hard work behind it.

You can validate your puzzle solution with certitude.

Congrats to atc for the FTF.