After 17 months of studying alternatives for the uncompleted lines of the Metro subway, a regional task force voted yesterday to recommend to the federal government that a full 100-mile Metro system be completed essentially as planned.

The vote came after the boards and councils of every city and urbanized country in the Washington metropolitan area had decided, in essence, that the Metro subway is a cost-effective part of any solution for this region's transporation problems.

While yesterday's reaffirmation of the 10-year-old decision to build Metro is an important political statement, it does not provide the money to do the entire job.

The full 100-mile system, with the modifications approved yesterday, probably would cost to $6 billion. That ex o $6 billion. That exceeds by slightly more than $1 billion the ceiling on Metro construction costs that U.S. transportation Secretary Brock Adams outlined in a January letter to regional officials.

That fact, and the potentially divisive conflicts it is certain to set off in the months to come, bubbled quickly to the surface yesterday after the vote was taken to recommend completing the system.

Joseph S. Wholey, chairman of the Metro board, who has assumed primary political responsibility for developing the financial plan, told other members of the regional task force yesterday that "we are also going to have to take into account the financial realities."

The financial plan, he said, must include at lease one proposed initial Metro system that fits within Adams' ceiling on costs. Clearly, that system would fall short of the 100 miles, perhaps by as much as 20 miles.

The question that will be divisive is: Whose Metro line is left out of the initial system?

"I don't feel this is the place and the time to pick and choose," said Joseph Alexander of the Fairfax County Board.". . . I'm not in any position to do that," Alexander is a vigorous supporter of the entire Metro system, but particularly of the line to Franconia from downtown Alexandria. That line is generally regarded as the one most susceptible to an early cut.

Francis B. Francois, chairman of the regional task force and a Prince George's County Council member, adjourned the meeting for one week, negotiations will doubtless be held on the cost issue. Another problem also must be solved in Prince George's County.

The County Council, in a last-minute vote a week ago, introduced a whole new proposal on one route. It suggested a two-line arrangement in the south county area on the line from Anacostia, with terminals at both Rosecroft Raceway and Branch Avenue. It had been expected to choose one terminal or the other, not both.

The regional task force yesterday, in voting its approval for the full 100-mile system, included in its motion the instruction that Prince George's County must designate one line or the other as primary, or the task force will make that choice itself next week.

Both lines have been studied, but they have not been studied together, and task force members are anxious to complete their work. The County Council is expected to discuss the matter at its regular Tuesday meeting.

The full system recommended by the task force yesterday contains these features:

The Springfield station in Fairfax County adjacent to the beltway has been eliminated. The Franconia station, just southeast of Springfield Mall, will be renamed Franconia-Springfield. Otherwise, the line is unchanged.

The route to western Fairfax County from Arlington will terminate at Vienna, as planned, instead of at Tysons Corner, as proposed. However, land acquisition for a future Tysons Corner route will be studied.

The Greenbelt route will be built with at least three changes. The Chillum station has been moved and renamed West Hyattsville. The Prince George's Plaza Station has been relocated so it is directly across East-West Highway from that shopping center. The College Park station will be either eliminated or relocated away from an established residential area.

Not part of the study but part of the problem are undecided route alignments within the District of Columbia from the Columbia Heights Station to the Prince George's County line. Furthermore, D.C. officials have promised that the line crossing Fort Totten Park at the Fort Totten station will be underground instead of elevated as plans now show.

The Branch Avenue-Rosecroft route within the District of Columbia has been realigned, regardless of what happens in Prince George's County. The route was to have run along Suitland Parkway after crossing the Anacostia River. Now, it would cut south along Martin Luther King Jr. Avenue and then through St. Elizabeths Hospital before proceeding to the county along Wheeler Road.

Increased parking will be planned for a number of outlying stations.

The Shady Grove and Glenmont lines, both in Montgomery County, were not part of the study. However, the extension of the operating Red Line from Silver Spring to Glenmont will remain a significant issue as the financial plan develops because - at an estimated $370 million - it is the most expensive per mile of any of the suburban segments. Simple mathematics demonstrates that if Glenmont is not built, more than one other line might be.

"Glenmont money is the key," Wholey said to a colleague as the metting was breaking up yesterday. "It may drive us apart."

The regional task force is made up of officials from the Metropolitan Washington Council of Governments, the Metro Transit Authority and the regional Transportation Planning Board. The task force was formed in 1976 after the Urban Mass Transportation Administration (UMTA), a part of Adams' department, demanded the restudy.

That demand included the Glenmont line, but Montgomery County Executive James P. Gleason and other Maryland officials have been able to beat back all attempts at putting the line into the study.

However, an independent study of cost-saving measures on the line has been made and those results must be included in the financial plan. Wholey and federal officials have agreed on an Aug. 31 deadline for the financial plan.

Twenty-three miles of Metro are now operating and another 37 are either under construction or completely financed. Five more miles have federal blessing; the Glenmont line is another five miles. The study itself dealt with the remaining 30 miles: Gallery Place to Greenbelt; Anacostia to Branch Avenue; King Street to Franconia, and Ballston to Vienna.

In each of the four lines studied the consulting firm of Peat, Marwick, Mitchell & Co. predicted operating and construction costs for either Metro or some alternative - more buses, trolleys, expanded commuter rail, etc. The goal was to provide the same level of public transportation in each corridor that Metro would have provided, and then compare cost effectiveness.

Essentially, the study discovered that the higher cost of building Metro (mostly with federal money) was offset by lower operating costs over the long term. The lower costs of a bus-intensive system were offset by higher operating costs and more frequent replacement costs (more local money).

A central question is whether area politicians will raise fares along with inflation. If they raise fares at only half the rate of inflation - which has been the reality in recent years - the subsidized operating costs increase dramatically.

For example, Peat, Marwick found that in 1990, the cost of operating the total bus and rail system would be $90 million annually if fares track inflation, but would be $301 million if fares were raised at only half the rate of inflation. The financial plan will address that question.

Metro boosters have insisted that the study has just delayed construction, and thus driven costs up because of inflation. Sen. Charles McC. Mathias (R.Md.) called yesterday for a General Accounting Office investigation of "excessive delays" at UMTA.

"Today they voted on the wish list," said a knowledgeable area official after the meeting. "Now is when the blood-letting really begins."