Solving Non-linear Overdetermined System of Equations

Question

I have a problem similar to The best fit for variables in a number of equations? but my system is nonlinear i.e.:

$$A_1 * X * Y = B_1$$

$$A_2 * X * Y = B_2$$

$$...$$

$$A_n * X * Y = B_n$$

Are there any methods to solve this system for $X$ and $Y$?

Answer 1

Reposting comment as answer, owing to clarification and so the post is properly marked as being answered.

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No, since you just have that $$XY=\frac{A_1}{B_1}= \cdots =\frac{A_n}{B_n} \equiv \text{constant}$$ If $XY=3$ for instance, you don't know whether $X=3$ and $Y=1$ or $X=Y=\sqrt 3$ or any other factorization.