Rezolvare problema prin metoda sistemului

Stiind ca 3a/5b =0.5  sa se calculeze (2a+3b)/(8a-4b)=?

Rezolvare:

{3a/5b=0,5

{2a+3b/8a-4b=?

dacă 3a/5b=0,5, atunci 6a/10b=1

Prin urmare, 6a=10b sau 3a=5b, iar a=5b/3

{3* 5b/3:5b=0,5

{2a+3b/8a-4b?

{b=0,5

{(2a+3*0,5)/(8a-4*0,5)

{b=0,5

{(2a+1,5)/(8a-2)

{b=0,5

{(2*5b/3+1,5) / (8*5b/3 -2)=(5/3+3/2)/(20/3-2)=(19/6)/(14/3)=19*3/14*6=19/14*2=19/28=1/2=0,5

prin urmare 3a/5b=0,5=2a+3b/8a-4b?