[tex]__________________________[/tex]
What we have to do is to find the number of pigs and chickens, given the two equations where the number of pigs is represented as the variable p and the number of chickens is represented as c.
Note: I fixed the second equation since it is written incorrectly
[tex]\sf c + p = 12 \\ \sf 4c + 2p = 56[/tex]
First, choose any equation and isolate any variable
[tex]\sf c + p = 12[/tex]
[tex]\sf c + \cancel{p - p} = 12 - p[/tex]
[tex]\sf c = - p + 12[/tex]
Second, substitute the value of c to the equation 4c + 2p = 56 and solve the equation
[tex]\sf 4( - p + 12) + 2p = 56[/tex]
[tex]\sf - 4p + 48 + 2p = 56[/tex]
[tex]\sf - 2p + 48 = 56[/tex]
[tex]\sf - 2p + \cancel{48 - 48} = 56 - 48[/tex]
[tex]\sf - 2p = 8[/tex]
[tex]\sf \frac{ - 2p}{ - 2} = \frac{8}{ - 2} [/tex]
[tex]\sf p = - 4[/tex]
Third, substitute the value of p to the equation c = -p + 12
[tex]\sf c = - ( - 4) + 12[/tex]
[tex]\sf c = 4 + 12[/tex]
[tex]\sf c = 16[/tex]
[tex]\sf SS: \{ (16, - 4)\}[/tex]
↬ Hence, the number of pigs is 4 while the number of chickens is 16.
