Question

Calculati x,y,z. a)x/y=3/5 si 2x+g=22 b)x/g=3/11 si 4x+2y=46 c)x/y=2/9 si 10x-2y=16 d)x/y=5/8 si 3x-2y=4
Va rog mult ajutatima :(

Answer 1

a) $\frac{x}{y} = \frac{3}{5}$  adica:

$\frac{x}{3} = \frac{y}{5}$ = 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) $\frac{x}{y} = \frac{3}{11}$  adica:

$\frac{x}{3} = \frac{y}{11}$ = 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=$\frac{23}{17}$ deci

x=$\frac{3*23}{17}$ = $\frac{69}{17}$
y=$\frac{5*23}{17}$ = $\frac{115}{17}$

c) $\frac{x}{y} = \frac{2}{9}$  adica:

$\frac{x}{2} = \frac{y}{9}$ = 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) $\frac{x}{y} = \frac{5}{8}$  adica:

$\frac{x}{5} = \frac{y}{8}$ = 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