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Solve: x^2+y^2=10 and xy=3

Answer: (+/-3, +/-1) or (+/-1, +/-3)

Yes, all of those answers work. You can prove that by substitution.

You can also derive it by substituting 3/x for y in the first equation.

x^2 + 9/x^2 = 10
x^4 - 10x^2 +9 = 0
(x^2-9)(x^2 - 1) = 0
(x+3)(x-3)(x+1)(x-1) = 0

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