1996 Buick Century Can low oil "BURN" up Antifree

1996 Buick Century 6 cyl

My Mom was telling me her car had a warning light lighting up for a few seconds here and there, she tells me it was on the left side with Squiggly lines, so I start the car and see that the squiggly line one was the TEMP for the Coolant, which I thought was a bit odd as she had just come home from driving a while yet the temp gauge was low, well it was nite so I would take a look in the morning. Anyway I open the hood and look at the coolant resiivour and it was DRY, so I figure either something is leaking or maybe it evaporated, anyway, I tell her we need to get some coolant in there, and see what happens. So as we are driving to Pep Boys she points to the dash and says see the light is on, I look down and its NOT the coolant its the OIL light, thank god we were right at the store, Long store short I Needed to put 3 quarts in to get the right oil level along with better part of a gallon of antifreeze. Everything seems to be fine and considering the car is old and has a slight valve cover leek I am going to keep an eye on it every couple weeks, but I was wondering could the engine have been compensating for the loss of oil buy "Burning" coolant? There is no lleaks so I am wondering where the coolant I KNOW the car had 2 months before went?