Question

Sa se rezolve sistemul de ecuatii:

$\frac{x!}{(x-y)!}= \frac{7x!}{(x-y+1)!}$

$\frac{6x!}{y!(x-y)!}= \frac{5x!}{(y+1)!(x-y-1)!}$

Mersi.

Answer 1

x!(x-y+1)! = 7x!(x-y)! => (x-y+1)!=7(x-y)!

(x-y+1)! = (x-y)!(x-y+1)

(x-y)!(x-y+1)=7(x-y)! => x-y+1=7 => x-y=6 (1)


6x!(y+1)!(x-y-1)!=5*y!(x-y)!

6(y+1)!(x-y-1)! = 5y!(x-y)!

(y+1)! = y!(y+1)
(x-y)! = (x-y-1)!(x-y)

6y!(y+1)(x-y-1)! = 5(x-y-1)!(x-y)
 
6(y+1)=5(x-y) => 6y+6=5x-5y (2)

x-y=6
6y+6=5x-5y =>  6y+6 = 5(x-y) => 6y+6 = 30 => 6(y+1)=30 => y+1=5 => y=4
x=10