Step-by-step explanation:
Let's assume that x = number of chickens and y = number of pigs.
[tex]80 \: heads = x + y[/tex]
Since there are 4 feet for pigs and 2 feet for chickens:
[tex]254 \: feet = 2x + 4y[/tex]
By substitution, let's rearrange the first equation:
[tex]x = 80 - y[/tex]
Substituting this equation to the second one:
[tex]254 = 2(80 - y) + 4y \\ 254 = 160 - 2y + 4y \\ 254 - 160 = 2y \\ 94 = 2y \\ y = 47 \: pigs[/tex]
Since we found the number of pigs already, let's substitute the value to any of the equations.
[tex]80 = x + y \\ 80 = x + 47 \\ 80 - 47= x \\ x = 33 \: chickens[/tex]
There are 32 chickens and 48 pigs.
To check if 3e are correct, let's use the second equation:
[tex]254 = 2x + 4y \\ 254 = 2(33) + 4(47) \\ 254 = 66 + 188 \\ 254 = 254[/tex]
Therefore, the values we found are correct.
