We could all save a lot of time (not to mention money) if we knew which airline was cheapest so let's cut to the chase. Sorry, no single airline is always the cheapest (no, not even that airline) and I can prove it with some random fare comparisons. The good news is, there's a simple method to help you find the cheapest carrier every time you fly, every place you fly.

As you will see, even the so-called ultra discount carriers don't always have the best ticket prices. The fares in the quiz below are for flights on arbitrary dates in April. Prices were found in late February on an airfare comparison search site and Southwest.com.

1. Which airline had the cheapest Friday-to-Sunday flight from Houston to Cleveland?

A. United

B. American

C. Southwest

D. JetBlue

The answer is A. United's price of $391 beat American's $408 and Southwest's $456, while tickets on JetBlue were more than $1,000. Both JetBlue and Southwest have excellent prices on many routes but not on this particular flight, on these particular days. Try again.

2. Which airline had the cheapest Friday-to-Sunday flight from New York to Ft. Lauderdale?

A. Spirit

B. JetBlue

C. Virgin America

Strictly speaking, the correct answer is A for Spirit's lowball price of $237; JetBlue cost $253 and Virgin America charged $335. Spirit's win, however, is a technicality. In the real world JetBlue's airfare of $253 wins, thanks to bag fees. A Friday-Sunday flight suggests a getaway trip and you will most likely want at least a carry-on bag, but that'll cost you $70 round-trip on Spirt. On JetBlue, carry-on bags are free.

3. Which airline had the cheapest Wednesday-to-Wednesday flight from Las Vegas to New York?

A. American

B. JetBlue

C. Spirit

D. Southwest

Another trick question. . Based on fare alone, American's $255 ticket price wins this round, followed by Southwest at $292. Spirit's $445 brings up the rear. However, if you want to check a bag ($50 round-trip) American's price balloons to $305. Conclusion: Southwest's $292 fare wins, thanks to its longtime policy of free checked bags.

Airfares can and do change all the time because airlines are constantly testing our demand for travel and willingness to absorb higher prices. A price you see today could change by tomorrow (or even by evening). Airlines have gotten very good at controlling capacity and prices; they had no choice in the modern era because no airline wants to wind up on page 30 of your online airfare search query.

So here's what you need to do, every time you shop for plane tickets: Always compare airfares.

The best approach is to use an airfare comparison search site and open up a second window for Southwest (the Texas-based carrier is the only airline that does not allow its prices on any other site). You'll be surprised at how different fares can be, depending on when you buy and when you need to fly.

If you only shop one airline – whether it's Southwest or Spirit or Frontier, or whatever your favorite discounter may be – you might get a good price. Or you might not. You will risk paying far more than you have to. Is it worth it?

And please, don't forget the baggage fees. They really can add up.

[More on this topic from Investopedia: An Insider's Guide to Finding Cheap Airline Tickets and Top Cheap Travel Websites.]

Rick Seaney is the CEO and cofounder of FareCompare