Do it orally

$3^x + 2^y = 985$

$3^x - 2^y = 473$

Let's add our two equations:

$2 × 3^x = 1458$

$3^x = 729$

$x = 6$

If we substitute this back into the first equation, we get:

$729 + 2^y = 985$

$2^y = 256$

$y = 8$

Hence, our answer should be:

$xy = 6 × 8 = \boxed {48}$

Orally, $3^x$ is between 473 and 985 so it must be 729. so x is 6

Now from 1st equation, $2^y=985-729$ which is bit more than 200. thus, it is 256 and y is 8

xy is 48