Afarm house shelter 11 animals some are goats and some are sucks altogether there are 34 legs how many of each animal there

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 

so far i think you have the right thing going for you just remember soh cah toh

step-by-step explanation:

sine over hypotenuse

cosine   equals adjacent

tangent over hypotenuse