2025/021) Find integer solutions of the equation $2x - 3y = 8$

we can solve by fining GCD of 2 and 3 but here I shall solve it by a different approach 

We can rewrite this as

$3y = 2x -8$

RHS is even so LHS should be even or y should be even

So let $y =2k$

We get $6k = 2x -8$

Or x = $3k + 4$

So $x = 3k + 4$ and $y = 2k$ are parametric form of solution

by choosing any integer for k we can get particular solution

k = 1 gives (7,2)

k =2 gives (10,4)