Answer
$\{(-10,-6,25)\}$
Work Step by Step
1. Use elimination for the first two equtions $\begin{cases} 2x-3y=-2 \\ x+y=-16 \end{cases}$ , multiply 3 to the second equation, we have $\begin{cases} 2x-3y=-2 \\ 3x+3y=-48 \end{cases}$
2. Add up the two equations to get $5x=-50$, thus $x=-10$
3. Use the second equation to get $-10+y=-16$, thus $y=-6$
4. Substitute the results in the third equation to get $3(-10)-2(-6)+z=7$, thus $z=25$
5. Thus the solution set is $\{(-10,-6,25)\}$
