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I'm not sure what is exactly your concern about the bivariate Coppersmith method -- if it's about the theory, you'd better read the original paper.

As for your second question - the two polynomials modulo 1763 have the same set of zeroes, simply because one of them represents a multiple of the other. This can be seen from computing their resultant and observing that it's zero modulo 1763. Here is a code illustrating that

R.<a,b> = PolynomialRing(ZZ)
p = (25*a+11)*(27*b+1)
q = (17*(a+4)+10)*(19*(b+3)+9)
r = p.resultant(q)
t = r.polynomial(b).change_ring(Integers(1763))
print('resultant mod 1763:',t)