OS X El Capitan - Running Mavericks off of usb drive
If you have the Mavericks install app:


Copy the Install OS X Mavericks.app file to your desktop
Insert the flash drive you want the installation files to be copied to
Download this script, unzip it, then move the osx_10.9_bootable.sh file to your Desktop.
Open Terminal app, then type cd ~/Desktop/ and hit enter
Then type sh osx_10.9_bootable.sh and follow instructions then wait


If this was successful, restart your Mac and hold down the Option key then select the newly created installation drive to install Mavericks onto your external HDD.



(in this case, 0553225513 is my external hdd, which will be your flash drive)

After the installation you can reinstall OS X El Capitan on your Macbook.