Chapter 3.2, Problem 9P

$\left(a\right)$ Show that the functions $x\left(t\right)=3e^t+7e^{-t}$ and $y\left(t\right)=3e^t+21e^{-t}$ are solutions of the system

$x\text{'}=2x-y$,

$y\text{'}=3x-2y$,

Satisfying the initial conditions $x\left(0\right)=10$ and $y\left(0\right)=24$.

$\left(b\right)$ Use a computer to plot the graphs of $x$ and $y$ versus $t$.