Equation - animals

There are a total of 35 hens and rabbits in the yard. They have a total of 94 feet. Calculate (by equation) how many hens there are in the yard and how many rabbits.

Correct answer:

x =  23
y =  12

Step-by-step explanation:

$$\begin{gathered} x+y=35 \\ 2x+4y=94 \\ x+y=35 \\ 2\cdot x+4\cdot y=94 \\ x+y=35 \\ 2x+4y=94 \\ Pivot:Row1\leftrightarrow Row2 \\ 2x+4y=94 \\ x+y=35 \\ Row2-\frac{1}{2}\cdot Row1\to Row2 \\ 2x+4y=94 \\ -y=-12 \\ y=\frac{-12}{-1}=12 \\ x=\frac{94-4y}{2}=\frac{94-4\cdot 12}{2}=23 \\ x=23 \\ y=12 \end{gathered}$$

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