82. Tenglamalar sistemasini yeching: 6/x + 4/y = 5; 8/x − 2/y = 3.

Belgilaymiz: \(a=\frac{1}{x}\), \(b=\frac{1}{y}\). Sistema: \[\begin{cases}6a+4b=5,\\8a-2b=3.\end{cases}\] Ikkinchi tenglamani 2 ga ko‘paytiramiz: \(16a-4b=6\). Birinchi tenglama bilan qo‘shib, \(22a=11\), demak \(a=\frac12\), bundan \(x=2\). Birinchi tenglamaga qo‘yamiz: \(6\cdot\frac12+4b=5\), \(3+4b=5\), shuning uchun \(b=\frac12\), ya’ni \(y=2\).

Javob: \(x=2,\ y=2\).