In Seattle, an elderly widower fighting loneliness -- and the cost of maintaining his home in the face of increasing taxes and fuel costs -- has agreed to share it with a young male student.

The student, who makes it an unbreakable habit when he comes home from his busy class schedule to sit down and chat with his new housemate, benefits by having comfortable accommodations at much less than he might otherwise have to pay.

These unlikely housemates are part of a growing movement nationwide toward shared housing for the elderly. The elderly, it seems, are taking a lesson from the young, who for years have teamed up to rent apartments and houses to save money. If it works for those in their 20s, why not for those in their 60s, 70s or older?

But unlike the young, who almost always matched up with others of the same age, the elderly are welcoming housemates of all ages. This trend was outlined at a Gray Panthers conference in Chevy Chase over the week-end, which argued for changes in local, state and federal legislation to overturn zoning, tax and other restrictions to such living arrangements.

"In our house, there are nine persons," said Maggie Kuhn, founder in 1970 of the Panthers, who battle for the rights of the elderly. The age spread is 22 to 74, "and I'm the oldest." Her Germantown, Pa. home, she said, also includes "three cats, a poodle pup who has a lot to learn, a pair of parakeets, and two tanks of tropical fish."

Among the reasons the elderly give for sharing, said Stephen R. McConnell of the Andrus Gerontology Center at USC, are:

Financial. Many have a lot of equity in their homes, "but you can't eat equity. If they sell, they still have to find a place to live."

Companionship. "Living alone can be a drag."

Disability. The elderly may need help with heavier tasks or want someone around in case of an emergency. In San Jose, Calif, he said, a blind woman who was unable to cook for herself took in a deaf housemate. "When the doorbell rings, the one who can hear answers it and the one who can see. . ."

A new Seattle group, Homesharing for Seniors, is something of a roommate referral system for the elderly. "Young people have been doing it for years. Today more and more older adults are finding that shared housing suits their needs, too," the organization advertises.

But, warned spokeman Leah Dobkin, "Housesharing is not easy." She advices potential housemates to discuss in advance what each expects from the arrangement. One may want more privacy, another more sociability, she said. Often a first match doesn't work out.

McConnell noted that women in their 70s or 80s seem to prefer younger men as housemates over women "because they don't wash out their underwear and leave it hanging around."

In prestigious Back Bay Boston, the "shared Living Project" has just renovated a 19th-century townhouse with 15 private bedrooms where young and old can live together "in a mutually supportive environment," said spokesman Susan Stockard. The age range now is 9 to 82 with room rents at $130 to $215 a month.

David Harre, executive director of the Richmond Fellowship here, which opened a five-person house for the elderly in Mount Pleasant in 1977, is not so enthusiastic about intergenerational shared housing. He thinks the problems involved in that life style are compounded by the age differences.

Also, he has found that despite, the advantages of group living for the elderly, "scores of people" living lonely lives in private homes or apartments are reluctant to give up their autonomy "for something new." But those who do, he said, find their friendships multiplying. At Thanksgiving, they can sit down to large family-style meals in their home rather than at a church basement among strangers.