#constrained system of equations

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amber tundra
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I'm trying to solve this system of equations, except I would like to add a few additional constraints. I want to add that a,b,c, and d are only allowed to be between 0 and 1. How in the world would I go about solving this??? I've been trying to solve this for a good while and have no idea how to solve this with the additional constraints.

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amber tundra
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I know that the answer without constraints is

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but how do I add the constraints on a,b,c, and d and find an answer that constrains r,p,y, and t to between some values???