[latex] \left \{ {{x-1/y=2/3} \atop {x^2+1/y^2=10/9}} \right. [/latex]

{(x-1) /y =  2/3 {(x²+1) / y² = 10/9 y≠0  , у²≠0 {3(x-1) = 2y { 9(x²+1) =10y² { 3x-3  -2y=0 {9x²+9  - 10y² =0 {y = (3x- 3)/2      ⇒ y= 3/2 * (x-1) = 1.5(x-1) {9x²-10y² +9=0 9x²-10*(1.5(x-1))² +9 =0 9х² - 10* (1,5х - 1,5)² +9=0 9х² - 10 *(2,25х²  - 2*1,5*1,5х + 2,25) +9=0 9х² - 22,5х²  + 45х  -22,5+9=0 -13,5х²  +45х  - 13,5  = 0             |÷ (-45) 0.3x² - x  + 0.3 =0 D = 1  -  4*0.3*0.3= 1- 0.36=0.64= 0.8² x₁= (1+0.8)/(2*0.3)= 1.8/0.6=3 x₂ = (1-0.8)/ 0.6 = 0.2/0.6 = 1/3 y₁=1.5 (3-1) = 1.5*2 = 3 y₂= 1.5 (1/3 - 1)  = 3/2  *  (-2/3) = -1 Ответ: (3;3)  ;  (1/3 ;-1)