Perform the Gauss Jordan elimination on the augmented matrix
#A=((4,-4,4,|,-4),(4,1,-2,|,5),(-3,-3,-4,|,-16))#
I have written the equations not in the sequence as in the question in order to get #1# as pivot.
Perform the folowing operations on the rows of the matrix
#R1larr(R1)/4#
#A=((1,-1,1,|,-1),(4,1,-2,|,5),(-3,-3,-4,|,-16))#
#R2larrR1-4R2#; #R3larrR3+3R1#
#A=((1,-1,1,|,-1),(0,5,-6,|,9),(0,-6,-1,|,-19))#
#R2larrR2*6#; #R3larrR3*5#
#A=((1,-1,1,|,-1),(0,30,-36,|,54),(0,-30,-5,|,-95))#
#R3larrR3+R2#
#A=((1,-1,1,|,-1),(0,30,-36,|,54),(0,0,-41,|,-41))#
#R3larr(R3)/(-41)#
#A=((1,-1,1,|,-1),(0,30,-36,|,54),(0,0,1,|,1))#
#R1larrR1-R2; R2larrR2+36R3#
#A=((1,-1,0,|,-2),(0,30,0,|,90),(0,0,1,|,1))#
#R2larr(R2)/30#
#A=((1,-1,0,|,-2),(0,1,0,|,3),(0,0,1,|,1))#
#R1larrR1+R2#
#A=((1,0,0,|,1),(0,1,0,|,3),(0,0,1,|,1))#
Thus, #r=1#, #x=3# and #t=1#