The federal tax system takes money away from most Americans, but President Carter now wants to use it to as part of his welfare plan to channel billions of dollars a year in payments and special tax cuts back to working people.

About 18 million families - one in four - would receive $6.7 billion in "welfare" through the tax system, under the Carter proposals.

And some of this tax relief could go to families of four whose income is as high as $15,600 a yar.

The tax plan is a key part of the administration's proposed new welfare system, which would replace most of the present federal programs aiding the nation's poor, aged, handicapped and needy.

The tax system was mobilized to help working poor people in 1975, when Congress authorized cash payments or tax credits to families earning less than $8,000. In some cases, these credits functioned as a "negative income tax," since families whose credits were greater than their tax liability were eligible for a check for the difference from the government.

The present credit is 10 per cent of income up to $4,00. The benefit declines after that and disappears at $8,000 income.

The 1975 law devised by Sen. Rusell B. Long (D-La.) as a way of rewarding poor Americans who work rather than rrely on government welfare. Currently, benefits of $1.2 billion a year go to an estimated 6 million families.

The Carter welfare package, which has a central objective of encouraging poor people to go to work, drastically expands the Long program. The administration wants its new welfare system to take effect in 1980.

"The whole concern of this program is to support poor people and their children without damaging the incentive to work," said a Treasury Department official. Both Long, chairman of the Senate Finance Committee, and Rep. Al Ullman, chairman of the tax-writing House Ways and Means Committee, have indicated general agreement with the tax objectives of the welfare plan.

The attempt to blend tax and welfare law is only the last part of a long history of attempts to update and reform the country's complicated welfare system.

When President Nixon first broached his "family assistance plan" in 1969, it was considered radical because it committed the government to guaranteeing some money to Americans without any income. Several attempts to get Congress to accept this principle failed because a sharp split between conservatives and liberals in both parties.

When he annouced his welfare revision plan early this month, President Carter said that the current system discourages people from working, encourages families to break up (because of restrictions on aid to parents who live together) and had produced wide difference in the benefits available on various states.

His plan would abolish most of the basic federal public assistance programs, including food stamps, and replace them with a single cash payment from the government.

The disabled, aged and handicapped would get cash grants, and working poor people would get small cash grants equal to, or slightly larger than, the cash value of the food stamps they now get.

The Carter plan envisions a cut off of those kinds of conventional welfare benefits at around $9,500 of income for a family of four. However, "welfare" benefits throught the federal tax system would not disappear until the family's income reached $15,000.

Administration experts say the tax aid is aimed at providing a major incentive to poor Americans to go to work - and to keep working as their pay increases and welfare benefits diminish.

Under Long's plan, the tax credits decline after $4,000 of income, and disappear at $8,000. Carter aides say that discourages poor people from trying to increase their salaries much past the poverty line about $5,820a year for an urban family of four).

TThrefore, the Carter tax plan keeps the tax benefits increasing up to $9,000 of income. The 10 per cent credit or rebate up to $4,000 and $9,000. Thus, a taxpayer who gets no tax benefits at $8,000 under Long's plan would get $600 under Carter's.

The advantages of working are intended to be persuasive in Carter's over all welfare package. For instance a husband, wife and their two children would be eligible immediately for about $2,300 - about equal to their current food stamp entitlement - if nobody in the family worked.

But if that same family earned, say, $6,000, it would still be eligible for a cash payment from the government of about $1,500 (to cover what it gets now in food stamps aid), and would also get a $550 tax credit. So that family would have basic income of about $8,050. That is more than three times as much as the family that does not work. A $8,000 of earned income, the government payment would be down to $200 - but the tax credit would have increased to $600.

"We want to make it profitable to keep working, and the tax credit is very important in this," said one official. "We want to convince Congress that every dollar spent on the tax credit will save more than a dollar in welfare payments."

The administration says that its overall welfare program contains key improvements on one family assistance plan of the Nixon administration. Officials say their program greatly increases incentives to work and adds an extensive program to find jobs for welfare recipients.