81. Tenglamalar sistemasini yeching: 6/x + 2/y = 3; 9/x − 2/y = 2.

Belgilaymiz: \(a=\frac{1}{x}\), \(b=\frac{1}{y}\). Shunda sistema quyidagicha bo‘ladi: \[\begin{cases}6a+2b=3,\\9a-2b=2.\end{cases}\] Tenglamalarni qo‘shamiz: \(15a=5\), bundan \(a=\frac{1}{3}\). Demak, \(x=3\). Birinchi tenglamaga qo‘yamiz: \(6\cdot\frac13+2b=3\), ya’ni \(2+2b=3\), \(b=\frac12\). Shuning uchun \(y=2\).

Javob: \(x=3,\ y=2\).