show can find d and b s.t pd-bq=1 , p and q are coprime- GCF =1

(Context probably irrelevant but modular forms- to show that all rational numbers can be mapped to $\infty$) that is there exists a $\gamma = ( a b c d)$, sorry thats a 2x2 matrix, $\in SL_2(Z)$ with $det (\gamma) = ad-bc=1$ s.t $\gamma . t = at+b/ct+d = \infty$, where take $t= r$ , r a rational number. )

So I'm at the stage where I am just stuck on showing that $p$ and $q$ co prime implies that $b$ and $d$ can be found s.t $pd-bq=1$ , b and d integer.

I'm not sure how to do this? I think the argument should be obvious?

Many thanks in advance.