Aflati numerele rationale pozitive x si y, stiind ca:
a) x/3=y/8 si x+y=22
b)x/y=4/9 si 2x+3y=40
c) 5x= 3y si 4y - 3x=0,11


Răspuns :

Răspuns:

Explicație pas cu pas:

a)x/3=y/8 => 8x=3y

x+y=22 => x=22-y

Din prima ecuatie: y=8x/3

Introducem y in a doua

x=22-8x/3 => 3x=66-8x => 11x=66 => x=6 => y=22-x=22-6=16

b)Idem acelasi rationament

x/y=4/9 => 9x=4y => y=9x/4

2x+3y=40 => y=(40-2x)/3

9x/4=(40-2x)/3 => 18x=4(40-2x) => 18x=160-8x => 10x=160 => x=16

y=9x/4=9*16/4=36

c)5x=3y =>  => y=5x/3

4y-3x=0,11 => y=(0,11-3x)/4 =>

5x/3=(0,11-3x)/4 => 20x=3(0,11-3x)  => 20x=0,33-9x

29x=0,33  => x=29/0,33

y=5x/3=5*29/3*0,33=145/0,99