I am doing maths for fun and stumbled upon this amazing worksheet. The second last question is a Diophantine equation with three variables and the solution ends with the general solution to the equation. I understand everything except how they go from
to the "general solution of x and y" from the above equation to
I understand that they get $w=8+6k$ and $z=1+k$ from the solution $(8, 1)$ but how they get to the general solution of x and y is unclear to me.