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$\left \{ {{2^x+2^y=12} \atop {x-y=1}} \right. \left \{ {{2^x+2^y=12} \atop {x=1+y}} \right. \\ 2^{1+y}+2^y=12 \\ 3*2^y=12 \\ 2^y=2^2 \\ y=2 \\ x=1+2 \\ x=3 \\ \left \{ {{2^3+2^2=12} \atop {3-2=1}} \right. \\ (x,y)=(3;2)$
$\left \{ {{2^x*4^y=32} \atop {x-y=2}} \right. \\ \left \{ {{2^x*4^y=32} \atop {x=2+y}} \right. \\ 2^{2+y}*4^y=32 \\ 2^{2+y}*2^{2y}=2^5 \\ 2^{3y+2}=2^5 \\ 3y+2=5 \\ y=1 \\ x=2+1 \\ x=3 \\ \left \{ {2^3*4^1=32} \atop {3-1=2}} \right. \\ (x,y)=(3;1)$