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There isn't a universal way to do this, just like there isn't a universal way to solve nonlinear equations in one variable. A good place to start, however, would be to attempt to solve an equation for one of the variables, in terms of the other two. If you substitute that into the other equations, you will then have a system of two equations in two variables. Do this again, and you'll have a single variable equation that you'll hopefully know how to solve.

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Q: How do you solve three nonlinear equations in three parameters?
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