The equation x+y=2 has infinite number of solutions.  Consider it as a function y= 2-x, where the domain of y is a Set of real numbers.  This means x can have any value in the domain of real numbers.  For each such value of x, y will have a unique value, also a real number.  Since real numbers are infinite, the given equation will have infinite number of solutions.

 

                                                          ****