How do you solve this question without using substitution?

Determine all ordered triples of integers (xyz) which satisfy the system

(xy) (xyz) = 189

(y + z) (x + y + z) = 147

(z + x) (x + y + z) = 546


And if you're wondering, the solutions are (xyz) = (14, -5, 12) and (xyz) = (-14, 5, -12)

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