Problem: The pair of equations 3x+y=81 and 81x−y=3 has:
Answer Choices:
A. no common solution
B. the solution x=2,y=2
C. the solution x=221​,y=121​
D. a common solution in positive and negative integers
E. none of these
Solution:
3x+y=81=34∴x+y=4
81x−y=3=8141​∴x−y=41​
∴x=2+81​,y=2−81​
The correct choice is (E)