Problem:
The lines x=41y+a and y=41x+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