\(a,\dfrac{x}{3}=\dfrac{y}{4}=\dfrac{z}{5}\Leftrightarrow\dfrac{2x}{6}=\dfrac{3y}{12}=\dfrac{5z}{25}\) và \(2x+3y+5z=86\)

Áp dụng tính chất dãy tỉ số bằng nhau có:

\(\dfrac{2x}{6}=\dfrac{3y}{12}=\dfrac{5z}{25}=\dfrac{2x+3y+5z}{6+12+25}=\dfrac{86}{43}=2\)

+) \(\dfrac{2x}{6}=2\Rightarrow2x=2\cdot6=12\Rightarrow x=12:2=6\)

+) \(\dfrac{3y}{12}=2\Rightarrow3y=2\cdot12=24\Rightarrow y=24:3=8\)

+) \(\dfrac{5z}{25}=2\Rightarrow5z=2\cdot25=50\Rightarrow5z=50:5=10\)

Vậy -

\(b,\dfrac{x}{3}=\dfrac{y}{4}\Leftrightarrow\dfrac{x}{9}=\dfrac{y}{12}\left(1\right)\)

\(\dfrac{y}{6}=\dfrac{z}{8}\Leftrightarrow\dfrac{y}{12}=\dfrac{z}{16}\left(2\right)\)

Từ \(\left(1\right);\left(2\right)\Rightarrow\dfrac{x}{9}=\dfrac{y}{12}=\dfrac{z}{16}\Leftrightarrow\dfrac{3x}{27}=\dfrac{2y}{24}=\dfrac{z}{16}\) và \(3x-2y-z=13\)

Áp dụng tính chất dãy tỉ số bằng nhau ta có:

\(\dfrac{3x}{27}=\dfrac{2y}{24}=\dfrac{z}{16}=\dfrac{3x-2y-z}{27-24-16}=\dfrac{13}{-13}=-1\)

+) \(\dfrac{3x}{27}=-1\Rightarrow3x=-27\Rightarrow x=-27:3=-9\)

+) \(\dfrac{2y}{24}=-1\Rightarrow2y=-24\Rightarrow y=-24:2=-12\)

+) \(\dfrac{z}{16}=-1\Rightarrow x=-16\)

Vậy -.

\(c,x:y:z=2:5:7\Leftrightarrow\dfrac{x}{2}=\dfrac{y}{5}=\dfrac{z}{7}\Leftrightarrow\dfrac{3x}{6}=\dfrac{2y}{10}=\dfrac{z}{7}\) và \(3x+2y-z=27\)

Áp dụng tính chất dãy tỉ số bằng nhau có:

\(\dfrac{3x}{6}=\dfrac{2y}{10}=\dfrac{z}{7}=\dfrac{3x+2y-z}{6+10-7}=\dfrac{27}{9}=3\)

+) \(\dfrac{3x}{6}=3\Rightarrow3x=3\cdot6=18\Rightarrow x=18:3=6\)

+) \(\dfrac{2y}{10}=3\Rightarrow2y=3\cdot10=30\Rightarrow y=30:2=15\)

+) \(\dfrac{z}{7}=3\Rightarrow z=3\cdot7=21\)

Vậy -

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