AMC 12B 2006 Problem 8

The lines x=\dfrac{1}{4} y+a and y=\dfrac{1}{4} x+b intersect at the point (1,2). What is a+b ?

Answer Choices
A. 0
B. \dfrac{3}{4}
C. 1
D. 2
E. \dfrac{9}{4}