PreCalculuscheck answer
posted by Lucy .
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^29)(x^2  1) = 0
(x+3)(x3)(x+1)(x1) = 0