Change of variables in a system of differential equations

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Given the following system :

$x'' + ax' + cx = kf(t) + cy$

$y'' + by' + cy = hf(t) + cx$

where $a,b,c,k,h$ are costants. It seems straightforward to set $z = x + y$ in order to get an equation like $z'' + s z' = (k+h)f(t) $. Now the problem is that I cannot find a value for the parameter $s$ and I don't even know if it is actually possible to find such $s$. Could you kindly help me please? Many thanks