If you can line up the backrest's tubes with the silver bar on the outside of your bike, you could drill appropriate holes into the bar on the bike, to bolt on the backrest. It really depends on whether that silver bar, on your bike's seat, is strong metal! If it is plastic, it won't support the backrest. I would suggest rubber washers between the backrest, and the bar on the bike, to protect its finish; if you ever sell the bike without the backrest, a couple of holes are preferable, to holes with scratches...
Alternatively, you could use some aluminum bar stock, from a DIY store (aluminum is less expensive than steel, but not as strong, either; both should be available), and put holes into that, which match the bolts on the existing bar on the bike -- use some stand-off's to create a gap between it, and the bike's body (small diameter aluminum tubing can be cut to size as needed); attach the backrest tubing to the bar stock (stand-off's optional). The bar stock can have its ends rounded, and it can be painted, to dress it up on the bike. If you paint it black, the color will mask minor imperfections in the cutting/grinding of the bar stock.
Sometimes you just have to be creative...
Cheers!
1979 CB750K (sold, 2012, but not forgotten)
1983 Kawasaki 440 LTD Belt Drive (sold, 2011)
1993 Kawasaki Voyager XII
Locked
What ever it is, it needs to go if you want to mount the luggage rack.
