If you use a HELOC on your primary then the HELOC payments will be used with the Debt-to-Income for the new investment.

As I’m looking, my main concern is vacancy, since if I can’t get tenants to rent by the room I won’t be eliminating my housing cost.

Since you are in full time RE now and wanting to put debt on the homes, the outcome of the cash out refi will likely come down to your personal financial statement and income. 

@Susan Maneck - Yes, eliminating your rent can be a huge form of "yield", living in your property gives you huge tax incentives upon sale and in New York you would rather avoid anything over 4 units due to rent control and rent stabilization complexities as a newbie investor.

Short answer: they look at your DTI ratio (which considers your monthly debts), generally you cannot exceed 50% DTI with a new mortgage.

This would eliminate these issues. 

The demand for this cheap debt is insatiable.

The lender will look at the appraisal to determine fair market value and debt service coverage ratios to determine the qualify of the investment. 

Then once you contact the owners, you can sign a contract with them that says you will make up their back tax debt in exchange for their house. 

You make money holding Real Estate 4 ways: Cash Flow, Appreciation, Debt Paydown, Tax benefits.