Question

se da proportia x/y=1/2, cu x,y € Q+. Afla numarele x si y, stiind ca: a) x+y=6
b)y-x=6
c)3x+2y=42
d)2y-3x=6

Answer 1

din proportia x/2=1/2 obtinem y=2·x (*)

a) daca x+y=6, inlocuim pe y din (*) si obtinem:

x+2·x=6 <=> 3·x=6 =>x=6:2 => x=2,

revenim la (*) si y=2·2  => y=4.

b) y-x=6 <=> 2·x-x=6 <=> x=6

 => y=2·6, y=12.

c)3x+2y=42 <=> 3x+2·2x=42 <=> 3x+4x=42 <=> 7x=42 => x=42:7 => x=6.

=> y=2·6, y=12.

d) 2y-3x=6 <=> 2·2x-3x=6 <=> 4x-3x=6 <=> x=6 => y=2·6 => y=12.