Đáp án:

Áp dụng tính chất dãy tỉ số bằng nhau ta có

$\begin{array}{l}
a)x:y:z = 3:5:\left( { - 2} \right)\\
 \Rightarrow \dfrac{x}{3} = \dfrac{y}{5} = \dfrac{z}{{ - 2}}\\
 = \dfrac{{5x}}{{3.5}} = \dfrac{{3z}}{{\left( { - 2} \right).3}}\\
 = \dfrac{{5x - y + 3z}}{{15 - 5 + \left( { - 2.3} \right)}} = \dfrac{{ - 16}}{4} =  - 4\\
 \Rightarrow \left\{ \begin{array}{l}
x = \left( { - 4} \right).3 =  - 12\\
y = \left( { - 4} \right).5 =  - 20\\
z = \left( { - 4} \right).\left( { - 2} \right) = 8
\end{array} \right.\\
\text{Vậy}\,x =  - 12;y =  - 20;z = 8\\
b)\dfrac{x}{2} = \dfrac{y}{{ - 3}} \Rightarrow y = \dfrac{{ - 3}}{2}x\\
\dfrac{z}{3} = \dfrac{y}{4} \Rightarrow y = \dfrac{4}{3}z\\
 \Rightarrow \dfrac{{ - 3}}{2}x = y = \dfrac{4}{3}z\\
 \Rightarrow \dfrac{{ - 3x}}{{12}} = \dfrac{y}{{12}} = \dfrac{{4z}}{{3.12}}\\
 \Rightarrow \dfrac{x}{{ - 4}} = \dfrac{y}{{12}} = \dfrac{z}{9} = \dfrac{{x + y + z}}{{ - 4 + 12 + 9}}\\
 = \dfrac{{5,2}}{{17}} = \dfrac{{26}}{{85}}\\
 \Rightarrow \left\{ \begin{array}{l}
x = \dfrac{{26}}{{85}}.\left( { - 4} \right) = \dfrac{{ - 104}}{{85}}\\
y = \dfrac{{26}}{{85}}.12 = \dfrac{{312}}{{85}}\\
y = \dfrac{{26}}{{85}}.9 = \dfrac{{234}}{{85}}
\end{array} \right.\\
\text{Vậy}\,x = \dfrac{{ - 104}}{{85}};y = \dfrac{{312}}{{85}};z = \dfrac{{234}}{{85}}
\end{array}$

Đáp án:

 a. Áp dụng t/c............

x : y : z= z/-2

=>z/3 = y/5 = z/-2

=> 5x/3.5 = 3z/(-2).3

=> 5x-y+3z/ 15-5+(-2.3) = -16/4=-4

=> x = (-4).3 = -12

=> y = (-4) . 5 = -20

=> z = (-4) . (-2) = 8

b. Áp dụng t/c.......

x/2 = y/-3 => y = -3/2 x

z/3 = y/4 =>y = 4/3 z

=> -3/2 x = y = 4/3 z

=>-3x/12 = y/12 = 4z/3.12

=> x/-4 = y/12 = z/9 = x+y+z/ -4 +12+9 = 5,2/17 = 26/85

=> x= 26/85 . (-4)

=> y = 26/85 . 12= 312/85

=> z=26/85 . 9 = 234/85

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