SOLUTION: Find values of a, b, and c (if possible) such that the system of linear equations has a unique solution, no solution, and infinitely many solutions. (If not possible, enter IMPOSSI

Question 1122204: Find values of a, b, and c (if possible) such that the system of linear equations has a unique solution, no solution, and infinitely many solutions. (If not possible, enter IMPOSSIBLE.)
x + y = 4
y + z = 4
x + z = 4
ax + by + cz = 0

Answer by ikleyn(52776) (Show Source): You can put this solution on YOUR website!
.

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.

Solved.

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