given :reaction system: see maxima.code 
M= [[-1  0  0]
 [ 1 -1  0]
 [ 0  1 -1]
 [ 0  0  1]
 [-1 -1 -1]]
input lsq :experimental values
b= [-1.25  0.37  0.33  0.54 -2.41]
x= [1.18375 0.79    0.47875]
output,rates,experimental values of b
r1= 1.18375
r2= 0.79
r3= 0.47875