Respuesta :
Explanation:
Let the number of hens be
[tex]=x[/tex]Let the number of goats be
[tex]=y[/tex]The number of animals on the farm is
[tex]=19[/tex]This can be represented in an equation below as
[tex]x+y=19-----(1)[/tex]The number of legs given in the question is
[tex]=68[/tex]Hens have 2 legs
Goats have 4 legs
So the number of legs can be represented in the equation below as
[tex]2x+4y=68-----(2)[/tex]Step 1:
We will solve equations (1) and (2) simultaneously
[tex]\begin{gathered} x+y=19----(1) \\ 2x+4y=68----(2) \end{gathered}[/tex]From equation (1), we will make x the subject of the formula
[tex]\begin{gathered} x+y=19 \\ x=19-y-----(3) \end{gathered}[/tex]Step 2:
Substitute equation (3) in equation (2)
[tex]\begin{gathered} 2x+4y=68 \\ 2(19-y)+4y=68 \\ 38-2y+4y=68 \\ 38+2y=68 \\ collect\text{ similar terms, we will have} \\ 2y=68-38 \\ 2y=30 \\ divide\text{ both sides by 2} \\ \frac{2y}{2}=\frac{30}{2} \\ y=15 \end{gathered}[/tex]Hence,
The number of goats on the farm is
[tex]\Rightarrow15[/tex]