Analyzing 2-Lens System: Image Position, Magnification & Nature

[anizet]

Homework Statement

A convex lens (f1=300mm) is placed 200 mm from a concave lens (f2=-50mm). An object is placed 6m away form the convex lens. (the order is as follows: object - 6m - convex lens - 200mm - concave lens).
Determine the position, magnification and nature of a final image.

Homework Equations

for a single lens:
1/x+1/y=1/f (where x is distance from the lens to the object, y is the distance from the lens to the image),

The Attempt at a Solution

Should I analyze 2 lenses separately?
At first first lens, which gives the image at y1:
1/6m+1/y1=1/300mm
y1=~31.5cm, so it is placed behind the second lens! Should I now consider the second lens, starting from the point, where is the image? I mean:
1/x2+1/y2=1/f2
where x2=20cm-31.5 cm=-11.5cm ?
I'm a little bit confused..
And finally, how to calculate the magnification?

 

[Doc Al]

Should I analyze 2 lenses separately?
At first first lens, which gives the image at y1:
1/6m+1/y1=1/300mm
y1=~31.5cm, so it is placed behind the second lens! Should I now consider the second lens, starting from the point, where is the image? I mean:
1/x2+1/y2=1/f2
where x2=20cm-31.5 cm=-11.5cm ?

Exactly right. Solve it in steps. The image from the first lens becomes the object for the second lens (virtual object, in this case, since it's behind the second lens).

And finally, how to calculate the magnification?

Find the magnification for each, then multiply them.