this is really simple if you know what to do
let g stand for goat and d stand for duck, for obvious reasons...
you have 11 animals all together so
g+d=11
next you have 34 legs, with 4 legs per goat(4g) and 2 legs per duck (2d)
4g+2d=34
now you have your system of equations.
next solve for either d or g, im gonna choose the first equation cause its the simplest
d=11-g
now plug that into the second equation, so
4g+2(11-g)=34
now solve for g
34=4g+22-2g
34=2g+22
12=2g
6=g
so you have 6 goats
because there are only 11 animals, you can subtract 6 from 11 to get 5 ducks.
to check your answer, take the 6 goats and multiply by 4 legs to get 24 legs, then take the 5 ducks by 2 legs each to get 10 legs. add them together and you get 34 legs, so your answer is correct