{MARGIN} Technical question

Hello,
Quick question regarding margin trading on a bitcoin exchange (polo or Bitfinex or any other offering Margin trading).

**Scenario :**

*for the sake of this example, we will assume 1 btc = 1000.00 USD. and I will be trading on a USDBTC trading pair*

I deposit 1 btc in my margin account, and want to GO LONG @5x for 5000.00 USD.
I get a loan of 5 BTC from lenders of that exchange to fill my position.

The question is :

If I have BTC in my account, and lender provide BTC for margin trading, how does the exchange execute a BUY order when I open my position if I do not have USD ?

I assume there is some sort of USD/BTC conversion when opening my position and buying btc ?

I would really appreciate a technical answer.

PS : Please please please, do not just paste a link to a FAQ or refer me to the exchange calculator, I have checked before asking here and I need a technical reply, some sort of mathematical equation.