a) [tex] \frac{x}{y} = \frac{3}{5} [/tex] adica:
[tex] \frac{x}{3} = \frac{y}{5} [/tex] = k prin notatie, deci:
x=3k
y=5k si inlocuim in relatia:
2x+y=22, adica:
2*3k+5k=22
6k+5k=22
11k=22
k=2 deci
x=3*2=6
y=5*2=10
b) [tex] \frac{x}{y} = \frac{3}{11} [/tex] adica:
[tex] \frac{x}{3} = \frac{y}{11} [/tex] = k prin notatie, deci:
x=3k
y=11k si inlocuim in relatia:
4x+2y=46, adica (impartim la 2 ambii membri):
2x+y=23 si inlocuim x si y in functie de k de mai sus:
2*3k+11k=23
17k=23
k=[tex] \frac{23}{17} [/tex] deci
x=[tex] \frac{3*23}{17} [/tex] = [tex] \frac{69}{17} [/tex]
y=[tex] \frac{5*23}{17} [/tex] = [tex] \frac{115}{17} [/tex]
c) [tex] \frac{x}{y} = \frac{2}{9} [/tex] adica:
[tex] \frac{x}{2} = \frac{y}{9} [/tex] = k prin notatie, deci:
x=2k
y=9k si inlocuim in relatia:
10x-2y=16, adica:
5x-y=8 si inlocuim x si y in functie de k de mai sus:
10k-9k=8
k=8 deci
x=2*8=16
y=9*8=72
d) [tex] \frac{x}{y} = \frac{5}{8} [/tex] adica:
[tex] \frac{x}{5} = \frac{y}{8} [/tex] = k prin notatie, deci:
x=5k
y=8k si inlocuim in relatia:
3x-2y=4, adica:
3*5k-2*8k=4
-k=4
k= - 4 deci
x=5*(- 4) = - 20
y=8*(- 4) = - 32
