Consider the system, where kkk is a real constant:
x+y+z=4x+2y+3z=9x−y−3z=k\begin{aligned} x + y + z &= 4 \\ x + 2y + 3z &= 9 \\ x - y - 3z &= k \end{aligned}x+y+zx+2y+3zx−y−3z=4=9=k
Which statement about this system is correct?
Select all that apply.
k=−6k = -6k=−6 gives exactly one solution; every other value of kkk gives no solution.
k=14k = 14k=14 gives infinitely many solutions; every other value of kkk gives no solution.
The system has exactly one solution for every value of kkk.
k=−6k = -6k=−6 gives infinitely many solutions; every other value of kkk gives no solution.