We perform the Gauss Jordan elimination with the augmented matrix
#((5,5,-6,:,-21),(-2,1,-3,:,-18),(-1,6,-6,:,-25))#
#R1larr-R3# and #R3larrR1#
#((1,-6,6,:,25),(-2,1,-3,:,-18),(5,5,-6,:,-21))#
#R3larr2R3+5R2#
#((1,-6,6,:,25),(-2,1,-3,:,-18),(0,15,-27,:,-132))#
#R2larrR2+2R1#
#((1,-6,6,:,25),(0,-11,9,:,32),(0,15,-27,:,-132))#
#R3larr11R3-15R2#
#((1,-6,6,:,25),(0,-11,9,:,32),(0,0,-162,:,-972))#
#R3larr(R3)/(-162)#
#((1,-6,6,:,25),(0,-11,9,:,32),(0,0,1,:,6))#
#R2larrR2-9R3#
#((1,-6,6,:,25),(0,-11,0,:,-22),(0,0,1,:,6))#
#R2larr(R2)/(-11)#
#((1,-6,6,:,25),(0,1,0,:,2),(0,0,1,:,6))#
#R1larrR1+6R2-6R3#
#((1,0,0,:,1),(0,1,0,:,2),(0,0,1,:,6))#