Question

Tìm x;y nguyên dương biết (x;y thuộc N)

a)5x-2y=23

b) 8x +15y=250

Answer 1

a/ \(5x-2y=23\)

\(\Leftrightarrow y=\frac{5x-23}{2}=\frac{6x-12-\left(x+11\right)}{2}=x-6-\frac{x+11}{2}\)

Vì x, y nguyên nên \(\frac{x+11}{2}=t\in Z\)

\(\Rightarrow\left\{{}\begin{matrix}x=2t-11\\y=t-6\end{matrix}\right.\) (t nguyên tùy ý)

Để $x,y$ nguyên dương thì \(\left\{{}\begin{matrix}x=2t-11>0\\y=t-6>0\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}t>\frac{11}{2}\\t>6\end{matrix}\right.\)

\(\Leftrightarrow t>6\)

Vậy nghiệm nguyên dương \(\left\{{}\begin{matrix}x=2t-11\\y=t-6\end{matrix}\right.\)\(t\in Z;t>6\)