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)