We know $$x$$ and $$y$$ are integers such that $$-8 \leq x \leq 10 \& x+y=-4$$; we need to check from the options that which can be the value of the product $$x y$$.

From the options we would need $$-8 \leq x \leq 10 \& x+y=-4$$



A) $$x y=0-$$ which can be true for $$x=0$$ and $$y=-4$$ or for $$x=-4$$ and $$y=0$$.

B) $$x y=-9$$ - which cannot be the product of $$x$$ and $$y$$ as $$-9=(-1 \times 9) /(-3 \times 3)$$ cannot be the ralues of $$x$$ and $$y$$ as the sum of $$x$$ and $$y$$ needs to be -4 .

C) $$x y=9$$ - which cannot be the product of $$x$$ and $$y$$ as $$9=(1 \times 9) /(3 \times 3) /(-1 \times-9) /(-3 \times-3)$$ cannot be the values of $$x$$ and $$y$$ as the sum of $$x$$ and $y$ needs to be -4

D) $$x=\frac{1}{y} \Rightarrow x y=1-$$ which cannot be the product of $$x$$ and $$y$$ as $$1=(1 \times 1) /(-1 \times-1)$$ cannot be he values of $$x$$ and $$y$$ as $$x+y=-4$$

E) $$x y=130$$ - which cannot be the product of $$x$$ and $$y$$ as $$130=(10 \times 13) /(-26 \times-5) /(-10 \times-13) /(26 \times 5)$$ etc cannot be the values of $$x$$ and $$y$$ as the um of $$x$$ and $$y$$ needs to be - 4

Note: - Since a single answer is needed for this question, we do not need to check the remaining ptions once we get the correct answer.