Chapter 7.1, Problem 23P

Given that $x=\varphi \left(t\right),y=\psi \left(t\right)$ is a solution of the autonomous system $\frac{dx}{dt}=F\left(x,y\right),\frac{dy}{dt}=G\left(x,y\right)$ for $\alpha <t<\beta$, show that $x=\Phi \left(t\right)=\varphi \left(t-s\right),y=\Psi \left(t\right)=\psi \left(t-s\right)$ is a solution for $\alpha +s<t<\beta +s$ for any real number $s$.