Tìm x, y biết: x/3 - 4/ y = 1/5

\(\frac{x}{3} - \frac{4}{y} = \frac{1}{5}\)

⇔ \(\frac{4}{y} = \frac{x}{3} - \frac{1}{5}\)

⇔ \(\frac{4}{y} = \frac{{5x}}{{15}} - \frac{3}{{15}}\)

⇔ y(5x – 3) = 4.15

⇔ y(5x – 3) = 60

Lại có: 60 = (±1) . (±60) = (±2) . (±30) = (±3) . (±20) = (±4) . (±15)

= (±5) . (±12) = (±6) . (±10)

Mà 5x – 3 là số chia 5 dư 2 nên 5x – 3 ∈{-3; 2; 12}

Ta có bảng sau:

Vậy (x;y) ∈{(0;-20) ; (1;30) ; (3;5)}.