Tool system having a machining tool and a tool receptacle, wherein the machining tool has: a main body which is configured along a longitudinal axis and on a first end has a shank portion configured as a cutting portion, and on a second end has a receptacle portion for being received on a tool receptacle, said receptacle portion being configured so as to be in one piece with said shank portion; wherein the receptacle portion has a collar which projects in the radial direction and forms an axial abutment that runs transversely to the longitudinal axis, and an elastically enlargeable widening portion which is configured as a hollow shank and has an inner cavity that is open in the direction of the second end; wherein the external circumferential face of the widening portion has a plurality of separate clamping faces which run along the surface of a cylinder or cone that is coaxial with the longitudinal axis and at least in the circumferential direction are mutually separated by recessed depressions (19a, 19a', 19b, 19c, 19d); wherein the tool receptacle has a bore for receiving the hollow shank of the receptacle portion, and an axial bearing face for bearing the projecting collar, characterized in that the tool receptacle has an expansion mechanism which for radially widening the widening portion engages in the inner cavity of the widening portion, wherein the expansion mechanism, on regions that are mutually opposite in relation to the longitudinal axis, in a first direction pushes in a radially outward manner against the wall of the widening portion, and recessed depressions (19a, 19a') that mutually separate the clamping faces in the circumferential direction are in each case configured in these mutually opposite regions. a main body which is configured along a longitudinal axis and on a first end has a shank portion configured as a cutting portion, and on a second end has a receptacle portion for being received on a tool receptacle, said receptacle portion being configured so as to be in one piece with said shank portion; wherein the receptacle portion has a collar which projects in the radial direction and forms an axial abutment that runs transversely to the longitudinal axis, and an elastically enlargeable widening portion which is configured as a hollow shank and has an inner cavity that is open in the direction of the second end; wherein the external circumferential face of the widening portion has a plurality of separate clamping faces which run along the surface of a cylinder or cone that is coaxial with the longitudinal axis and at least in the circumferential direction are mutually separated by recessed depressions (19a, 19a', 19b, 19c, 19d); wherein the tool receptacle has a bore for receiving the hollow shank of the receptacle portion, and an axial bearing face for bearing the projecting collar, characterized in that the tool receptacle has an expansion mechanism which for radially widening the widening portion engages in the inner cavity of the widening portion, wherein the expansion mechanism, on regions that are mutually opposite in relation to the longitudinal axis, in a first direction pushes in a radially outward manner against the wall of the widening portion, and recessed depressions (19a, 19a') that mutually separate the clamping faces in the circumferential direction are in each case configured in these mutually opposite regions.