In Ramanujan's Notebooks Volume IV pg. 31 by Bruce C. Berndt, he describes an easy way to solve the general quartic by starting with the system$$x^2+ay=b\\y^2+cx=d\tag1$$ And solving for $x$; which gives you the depressed form of the quartic.
Now, I'm wondering whether Ramanujan had his own methods for solving the general cubic, quintic, etc.
And according to this MSE post, Ramanujan had his own method for solving a solvable quintics.
Question: What was Ramanujan's method for solving the solvable quintic and quartic?
Note: I mean the sort of sneaky system (like $(1)$) employed by Ramanujan, and some substitution.