What is the complexity of solving this specific System of Diophantine Equations?

Question

Given a set of linear Diophantine equations such that:

1. There are $3N$ equations.
2. The equations consist of $4N$ unique variables.
3. Each equation is of the form:

• ($a_0$+$a_1$)=($a_2$+$a_3$) or
• ($a_0$+$a_1$)=-($a_2$+$a_3$) (where, $a_i$ is a variable)

Query 1: What is the computational complexity of solving this system of linear equations (assuming a solution exists).

Query 2: Given an additional constraint that: The sum of all 'pairs' in each equation must be a positive integer (i.e. in above examples ($a_0$+$a_1$) and ($a_2$+$a_3$) must be a positive integer). What is the computational complexity of this system of linear equations with the additional constraint (again, we are promised a solution exists).

I could not find any reference related to the above problem or its computational complexity. Can someone please help with this?