Cho 2x-4y/3=4z-3x/2=3y-2z/4.Tìm x,y,z biết 2x-y+z=27 09/08/2021 Bởi Jade Cho 2x-4y/3=4z-3x/2=3y-2z/4.Tìm x,y,z biết 2x-y+z=27
Giải thích các bước giải: $\dfrac{2x-4y}{3}=\dfrac{4z-3x}{2}=\dfrac{3y-2z}{4}=\dfrac{2x-4y+3y-2z}{3+4}=\dfrac{2x-y+z-3z}{7}=\dfrac{27+z}{7}$ $\to\begin{cases}\dfrac{4z-3x}{2}=\dfrac{27+z}{7}\\ \dfrac{3y-2z}{4}=\dfrac{27+z}{7}\end{cases}$ $\to\begin{cases}x=\dfrac{-54+26z}{21}\\ y=\dfrac{6(z+6)}{7}\end{cases}$ $\to 2\dfrac{-54+26z}{21}-\dfrac{6(z+6)}{7}+z=27$ $\to z=\dfrac{783}{55}$ $\to x,y$ Bình luận
Giải thích các bước giải:
$\dfrac{2x-4y}{3}=\dfrac{4z-3x}{2}=\dfrac{3y-2z}{4}=\dfrac{2x-4y+3y-2z}{3+4}=\dfrac{2x-y+z-3z}{7}=\dfrac{27+z}{7}$
$\to\begin{cases}\dfrac{4z-3x}{2}=\dfrac{27+z}{7}\\ \dfrac{3y-2z}{4}=\dfrac{27+z}{7}\end{cases}$
$\to\begin{cases}x=\dfrac{-54+26z}{21}\\ y=\dfrac{6(z+6)}{7}\end{cases}$
$\to 2\dfrac{-54+26z}{21}-\dfrac{6(z+6)}{7}+z=27$
$\to z=\dfrac{783}{55}$
$\to x,y$