Simultaneous equations and Monte-Carlo Simulation

Hello,

I'm trying to run a Monte-Carlo estimation to verify some properties of a statistical estimator. To do this I want to simulate data which is based on simultaneous equations (e.g. i(1)=a*s(1)+b*s(2); s(1)=c*i(1)+d*i(2); s(2)=e*i(1)+f*i(2); i(2)=g*s(1)+h*s(2)). However, I want to run more than these 4 simultaneous equations but about 20-40. Thus I am not able to calculate the reduced form directly.

Thus, here is the question: How can I run a Monte-Carlo Simulation without the explicit reduced form?

Thank you very much!