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