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I don't have much experience with ODEs.

I have a simple system, which I believe is first order linear, similar to the following:

dA/dt = 2A + 3B - C

dB/dt = A + 2B - C

dC/dt = -2A + 5B - 2C

Now I would like to include the constraint that A + B + C = 1. How do I do this mathematically?