a)
$x=\dfrac y6=\dfrac z3$, $2x-3y+4z=24$ (đề như này mới đúng nhé)
Theo tính chất dãy tỉ số bằng nhau ta có:
$x=\dfrac y6=\dfrac z3=\dfrac{2x-3y+4z}{2.1-3.6+4.3}=\dfrac{24}{-4}=-6$
$\Rightarrow\begin{cases}x=-6.1=-6\\y=-6.6=-36\\z=-6.3=-18\end{cases}$
b) $\dfrac x{1,1}=\dfrac y{1,3}=\dfrac z{1,4}=\dfrac{2x-y}{2.1,1-1,3}=\dfrac{5,5}{0,9}=\dfrac{55}9$
$\Rightarrow\begin{cases}x=\dfrac{55}9.1,1=\dfrac{121}{18}\\y=\dfrac{143}{18}\\x=\dfrac{77}{9}\end{cases}$
c) $\dfrac x4=\dfrac y3\Rightarrow\dfrac{x}{4.5}=\dfrac{y}{3.5}\Rightarrow\dfrac x{20}=\dfrac y{15}$
$\dfrac y5=\dfrac z3\Rightarrow\dfrac y{15}=\dfrac z9$
$\Rightarrow\dfrac x{20}=\dfrac y{15}=\dfrac z9=\dfrac{x-y-z}{20-15-9}=\dfrac{-100}{-4}=25$
$\Rightarrow x=25.20=500, y=25.25=375,z=25.9=225$
d) $6x=10y=15z$
$\Rightarrow\dfrac{6x}{30}=\dfrac{10y}{30}=\dfrac{15z}{30}$
$\Rightarrow\dfrac x5=\dfrac y3=\dfrac z2=\dfrac{x+y-z}{5+3-2}=\dfrac{90}{6}=15$
$\Rightarrow\begin{cases}x=15.5=75\\y=15.3=45\\z=15.2=30\end{cases}$
5) $\dfrac{x-1}2=\dfrac{y+3}4=\dfrac{z-5}6$
$\Rightarrow\dfrac{-3(x-1)}{-3.2}=\dfrac{-4(y+3)}{-4.4}=\dfrac{5(z-5)}{5.6}$
$\Rightarrow \dfrac{-3x+3}{-6}=\dfrac{-4y-12}{-16}=\dfrac{5z-25}{30}=\dfrac{-3x-4y+5z+3-12-25}{-6-16+30}=2$
$\Rightarrow\dfrac{-3x+3}{-6}=2\Rightarrow x=5$
Tương tự $y=5,z=17$
6)
$\dfrac x2=\dfrac y3=\dfrac z5=\sqrt[3]{\dfrac{x.y.z}{2.3.5}}=\sqrt[3]{\dfrac{-30}{30}}=-1$
$\Rightarrow x=-1.2=-2,y=-3,z=-5$
