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Let the two digits be represented by a and b.
a x b = 12 then, b = 12/a.
a + b = 13.........after substituting for b this becomes :-
a + 12/a = 13.....multiply throughout by a :-
a2 + 12 = 13a....re-arrange :-
a2 - 13a + 12 = 0
This factors as (a - 12)(a - 1) = 0
When a - 12 = 0 then a = 12
When a - 1 = 0 then a =1
As we have already substituted for b then b can take one of theses values and the two numbers are 1 and 12.
Note : The solution can be easily determined from the values supplied in the question but the process of finding the answer will apply to any such problem.
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