Din direct proportionalitate, notam cu k valoarea comuna a rapoartelor:
[tex] \frac{x+1}{3} = \frac{2y+5}{5} = \frac{3z-2}{15} =k[/tex] (1)
si
x-2y+3z=32 (2)
Din (1) scoatem x, 2y si 3z in functie de k si inlocuim in (2):
[tex] \frac{x+1}{3} =k[/tex]
x=3k-1
[tex] \frac{2y+5}{5} =k[/tex]
2y=5k-5
[tex] \frac{3z-2}{15} =k[/tex]
3z=15k+2
Inlocuim in (2):
(3k-1)-(5k-5)+(15k+2)=32
3k-1-5k+5+15k+2=32
13k=26
k=2, deci:
x=3*2-1=5
2y=5*2-5=5
y=[tex] \frac{5}{2} [/tex]
3z=15*2+2=32
z=[tex] \frac{32}{3} [/tex]
