Children and horses

There are some children and horses in a field.  Together they have 39 heads and 122 feet.
How many children are in the field, and how many horses are in the field?

Correct answer:

a =  17
b =  22

Step-by-step explanation:

$$\begin{gathered} a+b=39 \\ 2a+4b=122 \\ a+b=39 \\ 2\cdot a+4\cdot b=122 \\ a+b=39 \\ 2a+4b=122 \\ Pivot:Row1\leftrightarrow Row2 \\ 2a+4b=122 \\ a+b=39 \\ Row2-\frac{1}{2}\cdot Row1\to Row2 \\ 2a+4b=122 \\ -b=-22 \\ b=\frac{-22}{-1}=22 \\ a=\frac{122-4b}{2}=\frac{122-4\cdot 22}{2}=17 \\ a=17 \\ b=22 \end{gathered}$$

Try another example