2006 AMC 12B 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 \qquad \text {(B) } \frac 34 \qquad \text {(C) } 1 \qquad \text {(D) } 2 \qquad \text {(E) } \frac 94

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.