Investors have been slow to come around to the idea that the U.S. economy might be able to withstand all the pressure put on it. With government stimulus programs having ended and the Federal Reserve having pushed interest rates sharply higher over the past 18 months, many believe that a recession is still inevitable.

Yet the stock market has continued to power higher, and the strength of major businesses across the economic spectrum is a key part of what's driving the rally. On Thursday morning, both Delta Air Lines (DAL 0.08%) and PepsiCo (PEP -0.62%) gave positive signs that they're seeing robust activity that's helping to support their respective companies. Below, you'll see more about what these two giants had to say and what it could mean for the broader economy.

Delta's time to fly

Shares of Delta Air Lines were up 4% early Thursday morning. The airline company was the first of its peers to report quarterly financial results, and the numbers it released were highly encouraging in showing the continued recovery in the once hard-hit industry.

Delta's second-quarter results had a lot of great news. Operating revenue hit a new record of $14.6 billion on an adjusted basis, rising 19% year over year. Total unit revenue was up slightly, but the big difference for Delta came from offering 17% higher capacity as passengers returned to the skies. Operating income also reached all-time highs, and adjusted earnings of $2.68 per share were far better than most investors had anticipated.

In particular, Delta saw a return to international travel. Passenger revenue for international travelers soared 61% year over year, hitting a new record for the spring season. Japan's reopening helped Delta in the trans-Pacific market, while both Latin America and Europe also showed solid rebounds. Moreover, Delta saw outsize gains in its premium and loyalty categories, suggesting that business travelers are also getting back on the road.

Delta believes the future looks similarly bright, projecting third-quarter revenue to climb 11% to 14% and earnings to be between $2.20 and $2.50 per share. That jibes with Delta's full-year forecast for 17% to 20% revenue growth and $6 to $7 per share in earnings, and the gains in the stock could bring Delta to its best levels since before the pandemic.

PepsiCo's not falling flat

Shares of PepsiCo were also higher early Thursday, posting a gain of better than 2%. The soft drink and snack food behemoth overcame some headwinds to generate impressive financial results in the fiscal second quarter ended June 17 and boosted its guidance for the remainder of the year.

PepsiCo reported a 10.4% rise in revenue year over year to $22.3 billion, with organic sales climbing 13%. Core earnings of $2.09 per share were up 15% from year-ago levels. Pricing power was the key component of PepsiCo's success, as unit sales volumes were actually down across both snack foods and beverages.

Sales gains were widespread across PepsiCo's global footprint, with Europe and the company's Africa, Middle East, and South Asia segment posting the strongest organic growth gains. The Frito-Lay North America unit also featured solid gains, with only the Quaker Foods unit lagging behind with minimal 2% growth.

In response to favorable conditions, PepsiCo now expects that it will see organic revenue grow 10% for the full year, up from an 8% projection previously. Core earnings per share should also rise 12% to $7.47, up $0.20 per share from its earlier guidance. That has many investors believing PepsiCo is a smart stock to buy.

Don't stop believing

It's easy to fall prey to pessimism about market conditions, and there's always the chance that markets will correct lower in the short run. Yet when businesses are strong, they support longer-term gains for their investors. That's a valuable lesson as more and more companies will release their latest results in the days and weeks to come.