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 x=1 works. If you included 2, you’d be saying that 2+1=\sqrt{2+3}, which isn’t true.

I assume this question arises because an easy way to solve the question above is by graphing y=x+1 and y=\sqrt{x+3}, right?

When you do that, you see that the graphs intersect at the point (1, 2). 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.

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