What are symbolic solutions to this system? Computer aided solutions are fine

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What are the symbolic solutions to this? I've only gotten approximations so far. I'm not very interested in how to solve it, I'm more interested in the solutions.

$$eb-dg-e(-e-b+e^2)+g=0$$ $$-dge+d+b(-e-b+e^2)-eg+1=b$$ $$ed+bg-e-dg(-e-b-e^2)=0$$ $$b-dg^2+d(-e-b+e^2)=-dg$$ Thanks!