Value of a+b+c

There are positive integers a,b, and c that satisfy this system of two equations:
What is the value of a+b+c?
Source: NCTM Mathematics Teacher, November 2006

Multiply the first equation by \textrm{-}1, the second equation by 2 and add them
43 =1\times 43 because 43 is a prime number.
a+b+c cannot equal 1 because a,b,c are positive integers.
a+b+c=43 and a+b-c=1.

Answer: 43


About mvtrinh

Retired high school math teacher.
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