First, convert your qcow image to a plain raw file:

qemu-img convert system.qcow -O raw system.raw

Then, create a dummy file (filled with zeros) of the size of extra space you want to add to your image. In this case, 4GiB (=10GiB – 6GiB):

dd if=/dev/zero of=zeros.raw bs=1024k count=4096

Fearlessly, add your extra space to your raw system image:

cat system.raw zeros.raw > big10G.raw

After that you can boot qemu to verify that added free space is available:

qemu -hda big10G.raw

Here is an real case example of what you can see in a qemu image on which Windows XP was installed:

Now, to grow your primary partition, I suggest you to download a Live CD like gparted Live CD or System Rescue CD, and boot on the .iso file with qemu:

qemu -hda big10G.raw -cdrom gparted-livecd-0.3.4-5.iso -boot d

This will allow you to grow and manipulate all your partitions safely thanks to parted and other open source system tools.

Finally you can convert back your raw image to a qcow one to not waste space:

qemu-img convert big10G.raw -O qcow growed-system.qcow

That’s all !

By the way, I think it’s possible to perform the second and third step of this how-to in a single operation using dd only.

Update: I missed it, but this issue is also described in the FAQ from the unofficial #qemu wiki (look at “How do I resize a disk image?” question).