<PRE><B>Question 655569</B>
x^2 + y^2 -9 = 2xy     (i)
x + y = 27             (ii)

Making x the subject in equation (ii) x = 27 - y
substitute x = 27-y into equation (i)

(27-y)^2 + y^2 - 9 = 2(27-y)y
729 - 27y -27y + y^2 + y^2 - 9 = 54y - 2y^2

Collect like terms and equate to zero
729 -9 - 27y -27y - 54y + 2y^2 +2y^2 = 0
4y^2 - 108y +720 = 0

Divide by 4
y^2 - 27y + 180 = 0
(y -12)(y-15) = 0
y=12; y=15
When y = 12; x = 15
When y = 15; x = 12</PRE>