How many ordered pairs?

Relevant wiki: Quadratic Diophantine Equations - Solve by Simon's Favorite Factoring Trick

$\begin{aligned} x+y - xy & = 49 & \small \color{#3D99F6} \text{Multiply both sides by }-1 \\ - x - y + xy & = -49 \\ xy - x - y + 1 & = -49 + 1 \\ (x-1)(y-1) & = -48 \end{aligned}$

Since $-48 = - 2^43$ , the number of ordered pairs of integers $(x-1,y-1)$ and hence that of ordered pairs of integers $(x,y)$ is $(4+1)(1+1)\times 2 = \boxed{20}$ .