Data:
Humans (x) = 2 Legs
Horses (y) = 4 Legs
74 Heads
196 Legs
Solving:
Addition method
[tex] \left \{ {{x + y =74} \atop {2x + 4y =196}} \right. [/tex]
Simplify by (-4) The first equation
[tex]\left \{ {{x + y =74(-4)} \atop {2x + 4y =196}} \right. [/tex]
[tex]\left \{ {{-4x - \diagup\!\!\!\!\!4y =-296} \atop {2x + \diagup\!\!\!\!\!4y =196}} \right.[/tex]
[tex]\left \{ {{-4x =-296} \atop {2y =196}} \right.[/tex]
[tex]-2x = -100.simplify(-1)[/tex]
[tex]2x = 100[/tex]
[tex]x = \frac{100}{2} [/tex]
[tex]\boxed{x = 50}[/tex]
Now, to find the number of horses, I will use the following equation and I will replace the found value, we will have:
[tex]x + y = 74[/tex]
[tex]50+y = 74[/tex]
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.
[tex]y = 74-50[/tex]
[tex]\boxed{y = 24}[/tex]
Answer:
Humans = 50
Horses = 24
