Diophantine equation = c?

Question

I'm used to solving the most basic equations not specifying the c,
but now I have

7106x + 4320y = 6

And I don't know how to calculate the 6

Answer 1

Your table shows that $$7106 \times (-383) + 4320 \times 630 = 2$$ How multiply both sides by $3$ to find $x,y$ such that $7106x+4320y=6$.