2175: humanity has expanded to the other planets, has found the ninth planet by observing slight gravitational disturbances from one direction (it turns out to have many habitable-ish moons that, if dark, are perfect for setting up colonies and space stations on), and population growth has since exploded. This instant massive expansion was kind of the ultimate land rush: instead of the government starting to sell the population land, an efficient cold-fusion torch drive was discovered that allowed for very fast travel to other planets - a few days at most to Jupiter and back, if the positions were favorable. The result is that everyone started moving to other planets, and with so much empty space and opportunities and whatnot, the population grew exponentially.
At first this was fine: countries of Earth just sent what supplies couldn't be made on other worlds out into space, and everything was fine. But exponential growth being exponential growth, by 2100 the carrying capacity of the entire Solar System was exceeded. Because of societal factors and random chance, the population hadn't the chance to level off into a logistic curve like regular demographics suggests, but instead rocketed into the range where all the combined farms of Europa, Titan, Mars, and Earth couldn't produce enough food to feed every mouth.
Obviously, people died. Riots broke out over food distribution, piracy skyrocketed even though there isn't anywhere to hide in space, and five hundred million people died before a solution was found.
The issue that I'm having is that I can't figure out what that solution is. By the time the food reserves and the backup plans are through, there are 80 billion living humans while the world-spanning farms of Europa and Mars and Titan can only sustain around ~40 billion; most of the excess are young adults born in the time of the Interplanetary Land Rush. In a less-extreme circumstance, the death rate would just increase a little bit and the population would level off, but obviously it won't level off by 50% without causing catastrophic damage to society.
I found I had this problem elsewhere, too, when designing supermassive galaxy-spanning alien empires: it fundamentally takes a large area of land per person to farm enough food to feed everyone, and there simply aren't enough planets whose conditions are perfect enough for any species to create enough farms to feed everyone without the population density being very low.
So: is there a way to circumvent the "carrying capacity" of planets for very advanced civilizations?
I feel like this question is a duplicate since it's so simple and seemingly basic, but I've searched the site a few times and found nothing. Sorry if this is a duplicate.