Answer
$\left\{\left(-3,2,1\right)\right\}$
Work Step by Step
We are given the system of equations:
$\begin{cases}
2x+y=-4\\
-2y+4z=0\\
3x-2z=-11
\end{cases}$
Use the elimination method. Multiply the first equation by 2 and add it to the second equation to eliminate $y$:
$\begin{cases}
2(2x+y)=2(-4)\\
-2y+4z=0\\
3x-2z=-11
\end{cases}$
$\begin{cases}
4x+2y-2y+4z=-8+0\\
3x-2z=-11
\end{cases}$
$\begin{cases}
4x+4z=-8\\
3x-2z=-11
\end{cases}$
$\begin{cases}
x+z=-2\\
3x-2z=-11
\end{cases}$
Multiply the first equation by 2 and add it to the second equation to eliminate $z$ and determine $x$:
$\begin{cases}
2x+2z=2(-2)\\
3x-2z=-11
\end{cases}$
$2x+2z+3x-2z=-4-11$
$5x=-15$
$x=-3$
Determine $z$:
$x+z=-2$
$-3+z=-2$
$z=1$
Determine $y$:
$2x+y=-4$
$2(-3)+y=-4$
$-6+y=-4$
$y=2$
The solution set of the system is:
$\left\{\left(-3,2,1\right)\right\}$
