So, the system is inconsistent.
Alternate method: The given system of equations is equivalent to the single matrix equation:
We shall reduce the coefficient matrix A to triangular form by E-row operations on it and apply the same operations on the right-hand side, i.e. on the matrix B.
Performing R2 → R2 - 3R1, we have
Performing R3 → R3 - 3R2, we have
The last equation of this system is 0x + 0y + 0z = -91. This shows that the given system is not consistent.
