I claim the ornamental design for an axle support bracket system, as shown and described.
FIG. 1 is a perspective view of an axle support bracket system;
FIG. 2 is an enlarged perspective view of a portion of the axle support bracket system illustrated in FIG. 1;
FIG. 3 is a left side elevational view of the portion of the axle support bracket system illustrated in FIG. 2 and which is a mirror image of the right side elevational view;
FIG. 4 is a front elevational view of the axle support bracket system;
FIG. 5 is a rear elevational view of the axle support bracket system;
FIG. 6 is a top plan view of the axle support bracket system; and,
FIG. 7 is a bottom plan view of the axle support bracket system.
The broken line shown in FIG. 1 is included for the purpose of illustrating environment and forms no part of the claimed design.