Animal heads and feet

When hunting hares and pheasants, hunters calculated that the animals caught had 36 heads and 100 feet. How many hares and how many pheasants do they catch?

Correct answer:

z =  14
b =  22

Step-by-step explanation:

$$\begin{gathered} z+b=36 \\ 4z+2b=100 \\ z+b=36 \\ 4\cdot z+2\cdot b=100 \\ b+z=36 \\ 2b+4z=100 \\ Pivot:Row1\leftrightarrow Row2 \\ 2b+4z=100 \\ b+z=36 \\ Row2-\frac{1}{2}\cdot Row1\to Row2 \\ 2b+4z=100 \\ -z=-14 \\ z=\frac{-14}{-1}=14 \\ b=\frac{100-4z}{2}=\frac{100-4\cdot 14}{2}=22 \\ b=22 \\ z=14 \end{gathered}$$

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