Simplify 2 separate shape files, but ensure common edges are identical

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I have 2 shape files.

One shows the political regions of Scotland.

The other shows the political constituencies of Scotland.

I need to simplify them to display in a webpage. The problem is that when I simplify them there are small discrepancies between edges on the regions compared with the same edges in the constituencies.

Is there any known tool or technique I could use to allow me to do the following:

• Simplify the regions shape file and the constituencies shape files
• Ensure all edges which are common to both are the exact same
• Export a simplified regions shape file and simplified constituencies shape file

Up til now I've been trying it with Mapshaper.org and experimented with the different simplification algorithms and ratios. But I've not found a way to make it sync common edges between both. I'm aware of QGIS and ArcGIS, but have no idea if this kind of thing would be possible in them.



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