Correct Answer  Option 4 : x ≥ y
Calculations:
From I,
x^{2} + 6x + 9 = 0
⇒ x^{2} + 3x + 3x + 9 = 0
⇒ x(x + 3) + 3(x + 3) = 0
⇒ (x + 3)(x + 3) = 0
Taking,
⇒ x + 3 = 0 or x + 3 = 0
⇒ x = –3 or x = –3
From II,
y^{2} + 9y + 18 = 0
⇒ y^{2} + 3y + 6y + 18 = 0
⇒ y(y + 3) + 6(y + 3) = 0
⇒ (y + 3)(y + 6) = 0
Taking,
⇒ y + 3 = 0 or y + 6 = 0
⇒ y = –3 or y = –6
Comparison between x and y (via Tabulation):
X

y

Relation

–3

–3

x = y

–3

–6

x > y

–3

–3

x = y

–3

–6

x > y

∴ x ≥ y