Pair me up

Find the number of ordered pairs of integers (x,y)(x,y) such that x23xy+2y2=27.x^2-3xy+2y^2=27.

Details and assumptions

For an ordered pair of integers (a,b)(a,b), the order of the integers matter. The ordered pair (1,2)(1, 2) is different from the ordered pair (2,1)(2,1) .

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