Question 1122204
.
<pre>
The  sub-system consisting of 3 (three) first equations has a unique solution x = y = z = 2.


When you add the fourth equation, it becomes

2a + 2b + 2c = 0,   or


a + b + c = 0.


Thus, 

    a)  if  a + b + c = 0,   then the system of 4 equations has a unique solution.


    b)  if a + b + c =/= 0,  then the system of 4 equations has no solution.


    c)  it is IMPOSSIBLE to this system to have infinitely many solutions.
</pre>

Solved.