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