Question

tìm các số nguyên x, y biết \(\frac{5}{x}\)- \(\frac{y}{3}\) = \(\frac{1}{6}\) ( x khác 0)

Answer 1

\(\frac{5}{x}-\frac{y}{3}=\frac{1}{6}\)

\(\Leftrightarrow\frac{5.3}{3x}-\frac{y}{3}=\frac{1}{6}\)

\(\Leftrightarrow\frac{5.3}{3x}=\frac{1}{6}+\frac{y}{3}=\frac{1}{6}+\frac{2y}{6}\)

\(\Leftrightarrow\frac{15}{3x}=\frac{1+2y}{6}\)

\(\Rightarrow\hept{\begin{cases}15=1+2y\\3x=6\end{cases}\Rightarrow\hept{\begin{cases}15=1+2y\\x=2\end{cases}}}\)

Thế x = 2 vào,ta có: 

\(\frac{15}{3.2}=\frac{15}{6}=\frac{1.2y}{6}\)

\(\Leftrightarrow\frac{15}{6}=\frac{2y}{6}\Rightarrow y=15:2=7,5=8\)