Data:
Humans (x) = 2 Legs
Horses (y) = 4 Legs
74 Heads
196 Legs
Solving:
Addition method
\(\left \{ {{x + y =74} \atop {2x + 4y =196}} \right.\)
Simplify by (-4) The first equation
\(\left \{ {{x + y =74(-4)} \atop {2x + 4y =196}} \right.\)
\(\left \{ {{-4x - \diagup\!\!\!\!\!4y =-296} \atop {2x + \diagup\!\!\!\!\!4y =196}} \right.\)
\(\left \{ {{-4x =-296} \atop {2y =196}} \right.\)
\(-2x = -100.simplify(-1)\)
\(2x = 100\)
\(x = \frac{100}{2}\)
\(\boxed{x = 50}\)
Now, to find the number of horses, I will use the following equation and I will replace the found value, we will have:
\(x + y = 74\)
\(50+y = 74\)
Number with incognito are to the left of the equality and numbers without incognito are to the right, remembering that when changing of side changes the signal.
\(y = 74-50\)
\(\boxed{y = 24}\)
Answer:
Humans = 50
Horses = 24
