[math-fun] Solving polynomial equations with roots, etc.

We know that there exists a formula that may use roots (and arithmetic operations) for solving polynomials for each degree through 4, and no higher. I. What's known about finding such a formula for solving *several polynomial equations in several variables* ? (The polynomials can be of different degrees in general, and the coefficients can be any complex numbers.) II. Wait! Let's go back a step and ask when such a system of polynomial equations is even *known to have a solution*. --Dan _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele