Solutions to Linear Diophantine equation $15x+21y=261$ Question 

How many positive solutions are there to $15x+21y=261$?

What I got so far
$\gcd(15,21) = 3$ and $3|261$
So we can divide through by the gcd and get:
$5x+7y=87$
And I'm not really sure where to go from this point. In particular, I need to know how to tell how many solutions there are.

you find all solutions from $ax+by=c$ with
$$x=x_0-\frac{b}{(a,b)}*t , y=y_0+\frac{a}{(a,b)}*t$$
$x_0$ and $y_0$ you find with the Euclidean algorithm backwards:
$15x+21y=261$ with $261=3*87$
21=1*16+6
15=2*6+3
6=2*3+0
$3=15-2*6=15-2*(21-1*15)=15-2*21+2*15=3*15-2*21$
multiplied with 87 we get
$261=261*15-174*21$
So $x_0=261$ and $y_0=174$
