First, consider the linear system

If $k = a$, the system has more than one solution. If $k = b$, the system has no solution. The closest integer of $|a - b|$ is c. M = mod(c,5), where mod(.) is the modulo operation. Next, consider the linear system

Its least squares solution is $\{\tilde{x}, \tilde{y}, \tilde{z}\}$. The closest integer of $(\tilde{y} \times 50)$ is N. What is the value of mod(M+N,5)?