The matrix form of the given system is
The given system of equations will have a unique solution iff the coefficient matrix is non-singular. Using R2 → R2 - R1, R3 → R3 - λR1, we get
Therefore, the coefficient matrix will be non-singular if
1 - 4λ + 6 - 6λ ≠ 0 ⇒ λ ≠ 7 10
Thus, the given system will have a unique solution if λ ≠ 7/10.
In case λ = 7/10 , Eq. (1) becomes
This shows that the equations are not consistent in this case.