Solving a telegraph equation problem I have the following problem, where I'm kinda lost what to do:

The voltage $v$ and current $i$ in an electrical cable along the
  $x$-axis satisfy the coupled equations
$$i_x + Cv_t+Gv = 0, \;\;\;\;\;\; v_x+Li_t+Ri= 0,$$
where C, G, L and R are the capacitance, (leakage) conductance,
  inductance, and resistance per unit length in the cable. Show that $v$
  and $i$ both satisfy the telegraph equation
$$u_{xx} = LCu_{tt} +  (RC+LG)u_t+RGu.$$

$u$ is a function of $x$ and $t$, i.e. $u = u(x,t)$. I have tried solving for $i$ and $v$, then taking the derivatives and inserting them into the telegraph equation, but it seemed I did something wrong...
How should I proceed here? Please let me know if you need more information. 
 A: Here is an answer to why $i$ satisfies the equation.
You want to prove
$$i_{xx} = LXi_{tt} + (RC+LG)i_t + RGi.$$
If you multiply your second coupled equation with $G$, you get
$$Gv_x + LGi_t + RGi = 0,$$
if you derive your first coupled equation by $x$, you get
$$i_{xx} + Cv_{tx} + Gv_x = 0.$$
From the two equations, if you subtract them, you have
$$LGi_t + RGi = i_{xx} + Cv_{tx}.$$
Now, If you expand the parentheses in the original equation you want to prove, in the end, you get the value $LGi_t + RGi$ which you can now replace, giving you
$$i_{xx} = LCi_{tt} + RCi_t + i_{xx} + Cv_{tx}.$$
after canceling out $i_{xx}$, this leaves the equation $$C(Li_{tt} + Ri_t + v_{tx})=0.$$
This is easy to prove as this is just the second of the coupled equations, derived by $t$ and multiplied by $C$.
A: Derive the first equation with respect to $x$. You get
$$ i_{xx} + C v_{tx} + Gv_x = 0.$$
Use the second equation and substitute $v_x$ into the last one, then derive the second equation with respect to $t$ in order to substitute $v_{xt}$ (obviously, Schwarz' theorem holds). Then rearranging terms you have the telegraph equation for $i$.
For $v$ is the same thing.
