Use method as the linetype, but then manually map it to the types of lines you want. You don't need to introduce another variable this way.

ggplot(df, aes(x=x, y=value)) +
    geom_point() +
    geom_line(aes(linetype=method)) +
    scale_linetype_manual(breaks=c("a","b"), values=c(5,3))