1)
{2x - y = 10 ⇒ у= 2х - 10
{2x²-3xy +y²=10
2х² - 3х × (2х - 10) + (2х-10)² = 10
2х² - 6х² + 30х + 4х² - 2*2х*10 +10² = 10
(2х² - 6х² + 4х²) + (30х - 40х) + 100 = 0
10х =10 - 100
-10х = - 90
х= -90 :(-10)
х= 9
у = 2×9 - 10
у=18 - 10
у = 8
ответ : (9 ; 8).
2)
{1/x +1/y = 1/6 x≠0 ; у≠0
{ x - 2y = -5
{(y+x)/xy = 1/6 |*6xy
{ x = -5 +2y
{6 × (y+x) = 1 × xy
{x = - 5 + 2y
6×(y + (-5) + 2y) = (-5+2y)×y
6(3y - 5) = -5y +2y²
18y - 30 +5y -2y²=0
-2y² + 23y -30 = 0
-2y² + 20y + 3y - 30 =0
-2y×(y -10) + 3×(y-10) =0
(y-10)(-2y +3) =0
y-10 = 0
y₁ =10
-2y +3 =0
-2y= -3
y = -3/(-2) = 3/2
y₂ = 1.5
x=-5+2*10
x = -5+20
x₁=15
x= -5 +2*1.5
x= -5 +3
x₂= - 2
ответ : (15 ; 10) ; (-2 ; 1,5)