Problem:
The lines x=41​y+a and y=41​x+b intersect at the point (1,2). What is a+b?
Answer Choices:
A. 0
B. 43​
C. 1
D. 2
E. 49​
Solution:
Substituting x=1 and y=2 into the equations gives
1=42​+a and 2=41​+b
It follows that
a+b=(1−42​)+(2−41​)=3−43​=(E)49​​
OR
Because
a=x−4y​ and b=y−4x​ we have a+b=43​(x+y).
Since x=1 when y=2, this implies that a+b=43​(1+2)=(E)49​​.
The problems on this page are the property of the MAA's American Mathematics Competitions