I did it because I knew this will be my ticket to riches beyond my wildest imagination... freedom, and bliss... and it paid off.So you can shortcut things, and with a bit of luck (a LOT of luck) you may make it... or you can follow a proven mathematical equation that WILL get you there.As a scientist and engineer, I can tell you that data, reliability, systems, and proof of concept ALWAYS is the better choice! 

Not to mention, just from a statistical/mathematical standpoint, it's quite likely that someone is coming in under the average long-term

Is it some ridiculous mathematical formula you need to understand the most complex Fourier expansion equations?

Many buyers paid too much for their homes, didn't understand the underlying mathematics involved, didn't understand the financial instruments they were using, used their properties like ATMs, and didn't understand enough about business and economic cycles to filter through all of the "buy buy buy . . . it's always a great time to buy" noise spewed by many others (including many RE pros) who also were equally clueless.The "no down-payment equals no 'skin in the game'" argument is a non sequitor.

A whole area of mathematics is dedicated to solving that type of actuarial question.

That is just basic mathematics.  

Think mathematically here.

I'm of the former opinion, and grateful to my parents for allowing me to graduate debt free from a great school.So, if we accept that paying off the debt with the HELOC is mathematically likely to deliver a favorable result, the next logical question is why not arbitrage the rate difference even further, and instead of paying the loans with the HELOC, buy rental investments, and use the cash flow to sustain the payments.And the answer is that absolutely this could work.

@Tim Wilson yeah it isn't the absolute most efficient mathematically speaking to buy something you'd be willing to live in, but it does tend to attract better tenants and gives some exposure to appreciation upside, while not depending on it to make the property work.

Always remember to do a mathematical estimate on your prospective property and try to look at it before you make an offer or at least have a clause in the sales contract that will allow you the time (usually 10 days) to make a detailed inspection and possibly back out of the deal without a penalty that will hurt y'all too much.Good luck to you both!