A second income is becoming increasingly necessary for buying a first home, according to a survey released this week by the U.S. League of Savings Associations.

For half of all those purchasing a first home, that second paycheck contributed more than 10 percent of the total household income. For a third of these home buyers, the supplementary earnings amounted to between 30 and 50 percent of the total household income.

Two paychecks are also important to a lesser extent for other house purchases. For 35 percent of these buyers, more than a tenth of the total household income comes from the secondary earner.

"Let's face it," said the league's chief economist, Kenneth J. Thygerson, "if you have no second income, you've got a problem."

In 1970, when a Harvard-MIT study said that 45 percent of the households could afford to buy an existing house, fewer women worked and many lending institutions were inclined to discount all or part of the wife's wages on the theory she was likely to give up employment.

The S&L League found that half of the sales in big metropolitan areas were to households with one or two people. Seventeen percent were made to singles, and 4 percent by unmarried couples.

In the smallest cities, the median household size was 3.4 persons and the proportions of singles and unmarried couples were smaller. In the big cities alone, single persons made up 18 to 19 percent of all buyers, while unmarried couples accounted for 7 percent.

In non-metropolitan areas, only 2 percent of the couples buying were not married.

The league study was intended to refute previous studies claiming that fewer and fewer Americans are able to afford homes at today's prices.

This claim is, "in the most part, simply untrue," said league president Joseph Benedict at a press conference this week. As proof he offered the evidence that "in spite of more than a decade of excessive inflation, American are buying homes in record numbers."

The Massachusetts Institute of Technology's Joint Center for Urban Studies found that only 36 percent of the nation's households could afford a median-priced, existing house in 1976, while about 45 percent could afford such a house in 1970 because housing increases outpaced income gains in the first part of the decade.

Another study by the Congressional Budget Office revealed that potential first-time home buyers were the hardest hit. A recent poll of 1, 416 adults by Citibank showed that 22 percent of the respondents postponed buying a new home last year because of economic reasons while only 14 percent said they did the previous year.

To refute this, the S&L league, which represents most of the country's thrift institutions, undertook its own study. It was based on 8,500 mortgage loan application filed at 200 savings and loans during the second quarter of last year. The league's study covers only customers successfully served by its members and does not take into account applications denied or never made, loan by other lenders or government-insured mortages.

Besides trying to disprove that houses are too expensive, the new study also tries to bury the myth that homeowners are all middle-aged and wealthy. More than one-third (36 percent) of all home buyers last year were less than 30 years old. More than half of those between 25 and 30 are either single or married without children and therefore, in Benedict's words, "have money to spend on homes."

The median household income of first-time buyers studied was $20,000. The median income last year of all Americans where the head of household was aged 25 and 34 was $13,995.

The median price of the homes first-timers in the survey bought was just about the same as the national median price for existing homes in 1976 - $38,100.

As a group, the home buyers' ratio of income to purchase price is not as disproportionate as it is for the country as a whole. The league did not tackle the question of whether individual households aare spending more proportionately for housing today than in the past.

The league emphasized that Americans from all economic strata are buying houses, so national facts and figures can be misleading. Distinctions should be made between city and country and first purchase and repurchase, and among geographic regions, the league cautioned.