SOLUTION: How do I solve this system? x²+y²=10 xy=3

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Question 615860: How do I solve this system?
x²+y²=10
xy=3
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
FOILing (x + y)^2 ___ x^2 + 2xy + y^2

substituting ___ (x + y)^2 = 10 + 2(3) = 16

taking square root ___ x + y = ± 4

xy = 3 ___ x = 3/y

x + y = 4 ___ substituting ___ 3/y + y = 4 ___ 3 + y^2 = 4y ___ y^2 - 4y + 3 = 0 ___ (y - 3)(y - 1) = 0
___ y = 3 AND 1 ___ solutions are (1,3) and (3,1)

x + y = -4 ___ same technique ___ solutions are (-1,-3) and (-3,-1)