How to solve this decryption algorithm given the encryption algorithm? Consider the following cryptosystem with plaintexts from the set $M$ and ciphertexts from the set $S$ with $M = S = \{0, 1\}^4$ . A plaintext $P = (P_1, P_2, P_3, P_4)$ is encrypted to a ciphertext $C = (C_1, C_2, C_3, C_4)$ as follows.
$C_1 = (a P_1 + P_2) \pmod 2$
$C_2 = (b P_1 + c P_2) \pmod 2$
$C_3 = (d P_3 + e P_4) \pmod 2$
$C_4 = ( P_3 + f P_4) \pmod 2$
The key is given as $k = (a, b, c, d, e, f)\in \{0, 1\}^6$, i.e., it holds $C = E(k,P)$.
a. Describe the decription algorithm.
b. Is the given system perfectly secure? Prove your answer.

I know that if $C_1 = a + P_1$ then $P_1 = a + C_1$. However because $C_1$ and $C_2$ use the same letters $P_1$ and $P_2$ (also in the case of $C_3$ and $C_4$), I don't know how to reverse them to get back $P_1$ and $P_2$
Here's a hint about the second part of the question:

b. Is the given system perfectly secure? Prove your answer.

Hint: what is the encryption of the plaintext $(0, 0, 0, 0)$?  If the ciphertext is something other than $(0, 0, 0, 0)$, what can we infer about the plaintext about that?