Răspuns
Explicație pas cu pas:
[tex]\{x,y,z\}~direct~proportional~\{3,4,5\}\Rightarrow \dfrac{x}{3}=\dfrac{y}{4}=\dfrac{z}{5}=k\Rightarrow x=3k,y=4k,\\z=5k\\2x-y+3z=102\\2\cdot 3k-4k+3\cdot 5k=102\\6k-4k+15k=102\\17k=102|:17\\\bold{k=6}\\x=3k\Rightarrow \bold{x=18}\\y=4k\Rightarrow \bold{y=24}\\z=5k\Rightarrow \bold{z=30}[/tex]
Răspuns
x = 18 ; y = 24 ; z = 30
Explicație pas cu pas:
{ x , y , z } d.p { 3 , 4 , 5 }
2x - y + 3z = 102
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x / 3 = y / 4 = z / 5 = K
x / 3 = K => x = 3 K
y / 4 = K => y = 4 K
z / 5 = K => z = 5 K
2 · 3 K - 4 K + 3 · 5 K = 102
6 K - 4 K + 15 K = 102
2 K + 15 K = 102
17 K = 102
K = 102 : 17
K = 6
x = 6 · 3 = 18
y = 6 · 4 = 24
z = 6 · 5 = 30
