Fairfax City voters yesterday overwhelmingly approved a $1.6 million bond issue to purchase four schools from Fairfax County, but rejected two other bond issues totaling $1 million to pay the county the city's share of the cost of a new courthouse and adult detention center.

By a vote of 1,756 to 137, city residents approved the school bonds, which will allow the city to purchase from the county Layton Hall, Westmore and Greenacres elementary schools and Sidney Lanier Intermediate School. When the purchase is completed, the city will own all the schools whithin its limits.

Voters rejected the proposed $900,000 bond issue to pay the city's share of the construction of the new county courthouse by a 1.073-to 783 vote. The $135,000 bond issue for the new adult detention center was defeated 1,116 to 713.

City Council members said last night the defeat of the courthouse and adult detention center bonds means the city will have to pay the county $110,000 annually for debt service until the voters approve the bonds at a later referendum.

Under an agreement with Fairfax County, the city has until June 30, 1983, to pass the two bond issues. If the bond issues are not approved by that date, the amount the city owed for the two facilities will be due and payable to the county in three annual installments.