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.

In your example, the solution set is {1}–only works. If you included 2, you’d be saying that , which isn’t true.

I assume this question arises because an easy way to solve the question above is by graphing and , right?

When you do that, you see that the graphs intersect at the point . But that 2, the y-value, isn’t part of the original equation—you introduced that as part of your solution. Therefore, it has no place in the solution set. The solution set should only show the x-value (or values, in a different question) that satisfy the equation.