find x and y so x^2 + y^2 = 2 would be correct

find x and y so x^2 + y^2 = 2 would be correct
The equation of a circle with a center at the origin is \(\displaystyle x^2 + y^2 = r^2\). So your equation is a circle centered on the origin with radius \(\displaystyle \sqrt{2}\). As Subhotosh Khan says, there are many (in fact an infinite number) of solutions.

-Dan
 
find x and y so x^2 + y^2 = 2 would be correct
By the distance formula, the solution is the set of all points that are exactly sqrt(2) units from a circle. This actually describes a circle.
 
find x and y so x^2 + y^2 = 2 would be correct.
Find x and y so that x + y = 2.

Finding a finite number of values that satisfy relationships among n unknowns generally requires specification of at least n relationships among those unknowns. You have two unknowns and one relationship. There is no reason whatsoever to assume that there is any finite set of solutions.
 
find x and y so x^2 + y^2 = 2 would be correct

Are there additional conditions you have omitted, such as that x and y must be integers? That would make it a somewhat more interesting problem.
 
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