{(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)