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How can I solve a set of boolean equationst to get a,b,c and d.

Like:

w = a*b*c*d x = !a*b*d y = !b*a*d + !c*a*d + !a*b*c + !d*!a*b z = a*c 

w, x, y, z are known.

This example above is very simple to solve via substituation. But what is with complex system of equations?

I have read this question: how to solve system of linear equations of XOR operation? but I have not xor - I have got not, and and or.

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