Question

determinați x y si z stiind ca x-y/2=y+z/8=z/6 si x+2z=48

Answer 1

x-y/2=y+z/8=z/6 = k
x-y/2 = k ==> x-y = 2k y+z/8 =k
y+z=8k z/6 =k
z= 6k x-y=2k y+z=8k z=6k
y+6k =8k
y=2k x-y=2k
x-2k=2k
x=4k x+2z=48
4k+2*6k=48
4k+12k=48
k=3 z=6*3=18
y=2*3=6
x=4*3=12

Answer 2

$\frac{x-y}{2} = \frac{y+2}{8} = \frac{z}{6} = \frac{x-y+y+2+z}{2+8+16} = \frac{x+2z}{16} = \frac{48}{16} =3$
$\frac{z}{6}=3 =\ \textgreater \ z=18 \\ x+2x=48 \\ x+2*18=48 \\ x+36=48 \\ x=12 [tex] \frac{x-y}{2} =3 \\ 12-y=6 \\ y=6$