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 (L) 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 (L), 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 ; 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 (L), in a first direction pushes in a radially outward manner against the wall of the widening portion , and recessed depressions 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 (L) 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 (L), 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 ; 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 (L), in a first direction pushes in a radially outward manner against the wall of the widening portion , and recessed depressions that mutually separate the clamping faces in the circumferential direction are in each case configured in these mutually opposite regions. <EOS>