Question

{x-1; y-2; z-3} d.p {1,2,3} si 2x + 3y - z = 55. Aflati x,y,z.

Answer 1

 [tex]\frac{x-1}{1}=\frac{y-2}{2}=\frac{z-3}{3} = ... k\\
\Downarrow\\
x-1=k deci x=k+1\;;\\ y-2=2k\;adica\;y=2k+2\\ z-3=3k\;deci\;z=3k+3\\ inlocuim\;si\;obtinem:2(k+1)+3(2k+2)- (3k+3)=55\\ 2k+2+6k+6-3k-3=55\\ 5k=50\;\;\Rightarrow\;\;\fbox{k=10} [/tex]
[tex]\Rightarrow\;\;x=10+1=11\;;\;y=2*11=22\;;\;z=3*11=33\;; [/tex]