Counting the number of solutions to a simple mapping problem

Question

Let $A:=\{8,3,-15,-5,-10\}$ and define the function

$$f:A\times A\to \Bbb Z,\quad (x,y)\mapsto x+y$$

How many solutions are for the equation $f(x,y)=-7$? List the solutions.

May I please have an explain ?

Answer 1

For each $x\in A$, you can compute what $y$ must be, if there is a suitable $y$:

$$ x+y=-7 \implies y = -7-x $$

Go through each of the possible $x$ and compute what the necessary $y$ must be. Check if that $y$ is in $A$; if it is, you have found a solution.