$$2^{ x+y }=16\\ 3^{ x }-3^{ y }=24$$
Steps I took:
$$\ln(2^{ x+y })=\ln(2^{ 4 })$$
$$(x+y)\ln(2)=4\ln(2)\Rightarrow x+y=4$$
$$\ln(3^{ x })-\ln(3^{ y })=\ln(24)\Rightarrow x-y=\frac { \ln(3)+\ln(8) }{ \ln(3) } $$
I tried to simplify these equations in a way that would make them easier to work with. I got stuck at the last step. I don't even if I went about this the right way. Please point me in the right direction so that I could find the solution by myself.