Showing values of x fall into a range or domain, when y is also part of the equation I am told to consider the relation: 
$$\frac{x^2}{\:20}+\frac{y^2}{5} = 1$$
(i) Show that the values of x for which the relationship is defined are given by:$-\sqrt{20}<=\:x\:<=\:\sqrt{20}$
(ii) Similarly, find the values of y for which the relation is defined.
Do I need to figure out what y is algebraically first and then try values of x that fall into the domain provided? And the next part it is saying.....I have no idea.

Your equation is
$$\frac{x^2}{20} + \frac{y^2}{5} = 1 \implies \frac{x^2}{20} = 1 - \frac{y^2}{5} \tag{1}\label{eq1A}$$
You have $\frac{y^2}{5} \ge 0 \implies -\frac{y^2}{5} \le 0 \implies 1 - \frac{y^2}{5} \le 1$. Thus, $\frac{x^2}{20} \le 1 \implies x^2 \le 20 \implies -\sqrt{20} \le x \le \sqrt{20}$. Similarly, since $\frac{x^2}{20} \ge 0 \implies 1 - \frac{x^2}{20} \le 1$, you have that $\frac{y^2}{5} \le 1 \implies y^2 \le 5 \implies -\sqrt{5} \le y \le \sqrt{5}$.
