2019 AMC 10B Problem 4

All lines with equation ax+by=c such that a,b,c form an arithmetic progression pass through a common point. What are the coordinates of that point?

\textbf{(A) } (-1,2) \qquad\textbf{(B) } (0,1) \qquad\textbf{(C) } (1,-2) \qquad\textbf{(D) } (1,0) \qquad\textbf{(E) } (1,2)

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