Given system of equations
2x+y+z=5
x−y+z=3
x+y+az=b
has no solution, D=∣2111−1111a∣=0⇒−2a−2−a+1+2=0⇒a=31
D1=∣53b1−1111a∣=5(−a−1)+−1(3a−b)+1(3+b)=−8a+2b−2
D2=∣21153b11a∣=2(3a−b)−5(a−1)+1(b−3)=a−b+3
D3=∣2111−1153b∣=2(−b−3)−1(b−3)+5(2)=7−3b
For the system to have no solution ⇒D=0,D3=0
∴a=31,b=37.