<｜begin▁of▁sentence｜>### Instruction:
As a cardiologist, imagine you have a patient with a heart condition, and you need to map out their heart's coordinates on a digital surface. You're provided with a digital image surface, akin to an X-ray of the heart, measuring 800x600 pixels. Your goal is to establish a Cartesian Coordinate System within the context of this surface, with dimensions reflecting a bounding box of the same size. The coordinate system should span from (0, 0) to (100, 100), mirroring the physiological range of the heart. Once initialized, you need to visualize and save this coordinate system overlay onto the image, which would help in further analysis and treatment planning.

To accomplish this task programmatically, you might utilize a Python library like NetworkX, leveraging its functionalities to establish the coordinate system and overlay it onto the image. Finally, you'd save the resulting image as 'coordinate_system.png' for future reference and analysis.
### Response:
import igraph as ig
import cairo

# Create a surface and context to draw on
surface = cairo.ImageSurface(cairo.FORMAT_ARGB32, 800, 600)
context = cairo.Context(surface)

# Define a bounding box and bounds for the coordinate system
bbox = ig.drawing.BoundingBox(800, 600)
bounds = (0, 0, 100, 100)

# Initialize the Descartes Coordinate System
dcs = ig.drawing.coords.DescartesCoordinateSystem(context, bbox, bounds)

# Draw something using the Descartes Coordinate System
# ... (drawing code goes here)

# Save the image
surface.write_to_png('coordinate_system.png')
<|EOT|>
