In question #10 of the backsolving chapter…

In question #10 of the backsolving chapter : in the xy plane, a line containing the points (a, a^3) and (10,40) passes through the origin. Which of the following could be the value of a?

I found the explanation in the answer key to be too time-consuming if I were to solve the equation with backsolving. Can you explain how to solve this question algebraically instead?

When talking about solution sets…

When talking about solution sets, do they consist of both the x and y coordinates or whatever satisfies the question? For example, in the problem x+1=√(x+3), would the solution set be {1} or {(1,2)}, or does it really not matter? Thank you.