aCu₂S + bHNO₃ →c Cu (NO₃)₂ + dH₂SO₄ + eNO +f H₂O

Cu: 2a = c------------------------------------(1)

S: a = d------------------------------------(2)

H: b= 2d +2f------------------------------------ (3)

N: b=2c + e------------------------------------(4)

O: 3b = 6c + 4d+e+f------------------------------------(5)

Substituting the value for a from 2^nd eqn into 1^st eqn

Substituting the value of  f in 2f = c + e
4e - 4c = c + e
3e = 5c
e = 5 and c = 3
Substituting the values of c and e in f = 2e - 2c
f = 10 - 6 = 4
Substituting the values of c and f in b = c + 2f
b = 3 + 8 = 11
Substituting the value of c in 2d = c
2d = 3
d = 3/2
Substituting the value of c in 2a = c
2a = 3
a = 3/2
 So a = 3/2, b = 11, c = 3, d = 3/2, e = 5, f = 4

Divinding the eqn by 2 to avoid fraction in chemical reaction

a = 3, b = 22, c = 6, d = 3, e = 10, f = 8

3Cu₂S + 22HNO₃ →6 Cu (NO₃)₂ + 3H₂SO₄ + 10NO +8 H₂O