How do I solve the below system of congruence? I'm new here , i want to solve the below system which $(x, y)$ are a paire in $\mathbb{N²}$.
$2x+2y= 1\bmod 10,4x+y= 7\bmod 10$
Thank you for your help

The first congruence $2x+2y=1\pmod{10}$ doesn't have any solution. If $(a,b)$ is a solution, $1=10k-2a-2b$.  RHS is even, LHS is odd.
