If equation 3x-2y=5 and ax+6y=10 have no common root, a=?

If two simultaneous equation are of the form:

\(ax+by=c\)
\(kx+ly=m\)

These equation will have no common root OR in other terms, will be parallel to each other when,
\(\frac{a}{k}=\frac{b}{l} \ne \frac{c}{m}\)---------------1

These equation will have infinite common roots OR have infinite solutions OR in other terms, will coincide/superimpose over each other when,
\(\frac{a}{k}=\frac{b}{l}=\frac{c}{m}\)----------------2

These equation will have just one common root OR in other terms, will intersect each other at one point when,
\(\frac{a}{k} \ne \frac{b}{l}\)-----------------------3

We are concerned about equation 1 here(No common root)

\(\frac{a}{k}=\frac{b}{l} \ne \frac{c}{m}\)

\(3x-2y=5\)
\(ax+6y=10\)

\(\frac{3}{a}=\frac{-2}{6} \ne \frac{5}{10}\)

Or just

\(\frac{3}{a}=\frac{-2}{6}\)

\(a=-9\)

Ans: "E"