Answer
$\{(-1,2,-4)\}$
Work Step by Step
1. Use elimination for the last two equations $\begin{cases} x+y-3z=13 \\ -3x+y-2z=13 \end{cases}$ , multiply -1 to the second equation, we have $\begin{cases} x+y-3z=13 \\ 3x-y+2z=-13 \end{cases}$
2. Add up the two equations to get $4x-z=0$, or $z=4x$
3. Use it in the first equation to get $4z+2(4x)=-12$, thus $x=-1$ and $z=-4$
4. Substitute the results in the second equation to get $-1+y-3(-4)=13$, thus $y=2$
5. Thus the solution set is $\{(-1,2,-4)\}$
