Chapter 5.2, Problem 25E

In Problems $25-28$, use the elimination method to find a general solution for the given system of three equations in the three unknown functions $x\left(t\right)$, $y\left(t\right)$, $z\left(t\right)$.

$\begin{array}{rll}{x}^{\prime }& =& x+2y-z,\\ y^{\prime }& =& x+z,\\ z^{\prime }& =& 4x-4y+5z\end{array}$