Question

[Trần Phương Thảo]

Tìm x,y,z biết:\(\frac{3\left|x\right|+5}{3}\)\(=\)\(\frac{3\left|y\right|-1}{5}\)\(=\frac{3-z}{7}\)\(và\)\(2\left|x\right|+7\left|y\right|+3z=-14\)

Answer 1

[Đinh Đức Hùng]

Đặt \(\frac{3\left|x\right|+5}{3}=\frac{3\left|y\right|-1}{5}=\frac{3-z}{7}=k\)

\(\Rightarrow\left|x\right|=\frac{3k-5}{3}\Rightarrow2\left|x\right|=\frac{6k-10}{3}\)

\(\Rightarrow\left|y\right|=\frac{5k+1}{3}\Rightarrow7\left|y\right|=\frac{35k+7}{3}\)

\(\Rightarrow z=3-7k\Rightarrow3z=9-21k\)

Vì \(2\left|x\right|+7\left|y\right|+3z=-14\)\(\Rightarrow\frac{6k-10}{3}+\frac{35k+7}{3}+\left(9-21k\right)=-14\)

\(\Rightarrow\frac{\left(6k-10\right)+\left(35k+7\right)+\left(27-63k\right)}{3}=-14\)

\(\Rightarrow\frac{-22k+24}{3}=-14\)

\(\Rightarrow-22k+24=-42\)

\(\Rightarrow k=\frac{-42-24}{22}=3\)

\(\Rightarrow\left|x\right|=\frac{3.3-5}{3}=\frac{4}{3}\Rightarrow x=-\frac{4}{3};\frac{4}{3}\)

\(\Rightarrow\left|y\right|=\frac{5.3+1}{3}=\frac{16}{3}\Rightarrow y=-\frac{16}{3};\frac{16}{3}\)

\(\Rightarrow z=3-7.3=-18\)