x - 3y +z = 0
2x -y + kz = 0
x +7y - 5z = 0
You asked:
Solve the system of equations:\[\begin{aligned}x - 3 y + z &= 0\\2 x - y + k z &= 0\\x + 7 y - 5 z &= 0\end{aligned}\]
MathBot Answer:
The system of equations has infinitely many solutions.
$$\begin{aligned}x &= 0\\y &= 0\\z &= 0\end{aligned}$$\(k\) is a free variable.