General Solution of Diophantine equation Having the equation:

$$35x+91y = 21$$

I need to find its general solution.
I know gcf $(35,91) = 7$, so I can solve $35x+917 = 7$ to find $x = -5, y = 2$. Hence a solution to $35x+91y = 21$ is $x = -15, y = 2$.
From here, however, how do I move on to finding the set of general solutions? Any help would be very much appreciated!
Cheers

On division by $7$ we get $5x+13y=3$
Now, by observation $13-5\cdot2=3$
So,  $5x+13y=3=13-5\cdot2$
$\implies 5(x+2)=13(1-y)\implies \frac{5(x+2)}{13}=1-y$ which is an integer
$\implies 13$ divides $5(x+2)$
$\implies 13$ divides $(x+2)$ as $(5,13)=1$
So, $x+2=13a$ where $a$ is any integer, $x=13a-2$
So, $13y=3-5x=3-5(13a-2)=13(1-5a)\implies y=1-5a$
We can use the convergent property to a continued fraction as follows:
$$\frac{13}5=2+\frac35=2+\frac1{\frac53}=2+\frac1{1+\frac23}=2+\frac1{1+\frac1{\frac32}}=2+\frac1{1+\frac1{1+\frac12}}$$
So, the previous convergent of $\frac{13}5$ is $2+\frac1{1+\frac11}=\frac52$
$\implies 13\cdot2-5\cdot5=1$
So, we can write $5x+13y=3=3(13\cdot2-5\cdot5)$
Can you take it from here?
