{x,y,z} i.p. {2,3,4}
2x=3y=4z=k
k-coeficient de proportionalitate
2x=k=>x=k/2
3y=k=>y=k/3
4z=k=>z=k/4
b)x+z-y=10
[tex] \frac{k}{2} + \frac{k}{4} - \frac{k}{3} = 10 \\ numitor \: comun \: 12 \\ \frac{6k}{12} + \frac{3k}{12} - \frac{4k}{12} = 10 \\ \frac{5k}{12} = 10 = > 5k = 120 = > k = 24[/tex]
x=k/2=>x=24/2=>x=12
y=k/3=>y=24/3=>y=8
z=k/4=>z=24/4=>z=6
a)x+y-z=7
[tex] \frac{k}{2} + \frac{k}{3} - \frac{k}{4} = 7 \\ aduci \: la \: acelasi \: numitor(12) \\ \frac{6k}{12} + \frac{4k}{12} - \frac{3k}{12} = 7 \\ \frac{6k + 4k - 3k}{12} = 7 \\ \frac{7k}{12} = 7 = > 7k = 7 \times 12 = > \\ 7k = 84 = > k = 12[/tex]
x=k/2=>x=12/2=>x=6
y=k/3=>y=12/3=>y=4
z=k/4=>z=12/4=>z=3
c)y+z-x=4
[tex] \frac{k}{3} + \frac{k}{4} - \frac{k}{2} = 4 \\ \frac{4k}{12} + \frac{3k}{12} - \frac{6k}{12} = 4 \\ \frac{k}{12} = 4 = > k = 4 \times 12 = > k = 48[/tex]
x=k/2=>x=48/2=>x=24
y=k/3=>y=48/3=>y=16
z=k/4=>z=48/4=>z=12
