Answer:
(x, y) = (5, -5)
Step-by-step explanation:
The equation can be rewritten as ...
9x^2 -90x +225 +x^2 +2xy +y^2 = 0
9(x^2 -10x +25) +(x +y)^2 = 0
9(x -5)^2 +(x +y)^2 = 0
The only way the sum of squares can be zero is for each square to be zero:
x -5 = 0
x +y = 0
Then x = 5 and y = -5.
