An organization of $10$ individuals is using Shamir Secret Sharing to protect their private data. The quorum they

have decided to use is $4,$ and they$$re working $($mod $17).$

$5$ members of the team come together to reveal the secret, and reveal the following information:

f $(1)=0,$ f $(5)=5,$ f $(6)=5,$ f $(8)=10,$ f $(10)=6$

$1.$ What is the minimum number of equations that we need to solve in order to recover the secret a$0?$

$2.$ Write down a system of linear equations that, if solved simultaneously, would let us recover the secret a$0.$

Note: there may be more than one possible answer for this part, and there is no need to actually solve the

system of equations.