Resolving the following system of equations:

Hello,

I am trying to numerically resolve the following system of equations:

f9_8 = (f10,9 - c9 * f9_10 -b9 * f9_9)/a9
f9_7 = (f10_8 - c8 * f9_9 - b8 * f9_8)/a8
f9_6 = (f10_7 - c7 * f9_8 - b7 * f9_7)/a7
...
f9_1 = (f10_2 - c2 * f9_3 - b2 * f9_2)/a2
f9_0 = (f10_1 - c1 * f9_2 - b1 * f9_1)/a1

where the following are known:
c1,c2,c3,...,c9
b1,b2,b3,...,b9
a1,a2,a3,...,a9
f10_1,f10_2,f10_3,...,f10_9
and also f9_10, f9_0

I am unsure as to how to proceed. Can anyone please help?

Thanks in advance,

Julien.