Note that this list is infinitely long, because x could be 12 and y could be -1, for example. Moreover, x could be 10.5 and y could be .5.
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There are 12 such pairs. Negative numbers are not allowed in algebra because they do not represent countable quantities. For example, suppose the unknowns represent the number of sheep on two different fields. It does not make sense for one field to have 13 sheep and the other to have -2 sheep, because there is no such thing as a negative sheep.