Again An Exponent?

$\large \begin{cases} 3^x + 2^y & = 985~~~ ........(1) \\ 3^x - 2^y & = 473 ~~~.......(2) \\ \end{cases}$

$(1) - (2):$

$\begin{aligned} 3^x + 2^y - 3^x + 2^y & = 985 - 473 \\ \Rightarrow 2(2^y) & = 512 \\ \Rightarrow 2^y & = 256 \\ \Rightarrow 2^y & = 2^8 \\ \implies y & = 8. \\ \end{aligned}$

Now substituting $y = 8$ in $(1):$

$\begin{aligned} 3^x + 2^8 & = 985 \\ \Rightarrow 3^x & = 985 - 256 \\ \Rightarrow 3^x & = 729 \\ \Rightarrow 3^x & = 3^6\\ \implies x & = 6. \\ \end{aligned}$

Hence $xy + 100 = (8)(6) + 100 = \boxed{148}.$

Let first one be equation i and second be eq ii. Adding i and ii .... we get $x = 6$ and subtracting i and ii we get $y = 8$ ... Now $xy = 48$ so $xy+100 = 148$ .. and thats the ans