Question

2x=3y=10z-2x-3y ; x-y+z = -15

Answer 1

Đặt \(2x=3y=10z-2x-3y=k\)

\(\Rightarrow\left\{{}\begin{matrix}x=\dfrac{k}{2}\\y=\dfrac{k}{3}\\\end{matrix}\right.\)

Lại có: \(10z-2x-3y=k\Rightarrow10z-k-k=k\)

\(\Rightarrow10z=3k\Rightarrow z=\dfrac{3k}{10}\)

Thế vào \(x-y+z=-15\) ta được:

\(\dfrac{k}{2}-\dfrac{k}{3}+\dfrac{3k}{10}=-15\)

\(\Leftrightarrow\dfrac{7k}{15}=-15\Rightarrow k=-\dfrac{225}{7}\)

\(\Rightarrow\left\{{}\begin{matrix}x=\dfrac{k}{2}=-\dfrac{225}{14}\\y=\dfrac{k}{3}=-\dfrac{75}{7}\\z=\dfrac{3k}{10}=-\dfrac{135}{14}\end{matrix}\right.\)