General Solution of Linear Diophantine Equation with 2 and more than 2 variable

Question

We know the theorem of linear diophantine equation from Bezout's identity that the solution is in ordered pair form:

$\left(x + m \dfrac{b}{\text{gcd}(a,b)}\,,\,y-m \dfrac{a}{\text{gcd}(a,b)}\right)$

For all integers $m$

Then, what is the general integer solutions for a linear diophantine equation with 3 or more than 3 variables?