AMC 12 2006b Problem 8

The lines $x = \frac 14y + a$ and $y = \frac 14x + b$ intersect at the point $(1,2)$. What is $a + b$?

$\text {(A) } 0 \text {(B) } \frac 34 \text {(C) } 1 \text {(D) } 2 \text {(E) } \frac 94$