19 geese and 11 horses
1) Note that geese and horses have each one, one head. So we can solve this problem by setting a system of Linear equations:
1 horse: 4 feet
1 goose: 2 feet
[tex]\begin{gathered} g+h=30 \\ 2g+4h=82 \end{gathered}[/tex]Notice the second equation relates to the number of feet each animal has.
2) We can solve this by using the Elimination Method, multiplying the first equation by -2
[tex]\begin{gathered} g+h=30 \\ 2g+4h=82 \\ --------- \\ -2g-2h=-60 \\ 2g+4h=82 \\ ------------- \\ 2h=22 \\ h=11 \end{gathered}[/tex]Now, we can plug into the 1st equation h=11
[tex]\begin{gathered} g+h=30 \\ g+11=30 \\ g+11-11=30-11 \\ g=19 \end{gathered}[/tex]So, there are 19 geese and 11 horses.
