Is it possible to mine bitcoins faster on CPUs with this strategy?
It's not clear what the strategy is. It just says "and solve the system of equations". 

The entire structure of cryptographic hashes like SHA256 is carefully designed to make doing this as difficult as possible, and there's not even a hint of how to solve that system of equations.

This is precisely what ordinary miners do, except they try to solve the system of equations by guessing possible solutions and seeing if they solve the equations. If there is a simpler way to solve them, what is it?