kuadrat dua variabel X²-3xy-2y²-2=0.dan x-y-2=0

Linear-Kuadrat Dua Variabel

x² - 3xy - 2y² - 2 = 0

x - y - 2 = 0

Dari pers.linear :
x = y + 2

Substitusi

(y + 2)² - 3(y + 2)y - 2y² - 2 = 0
(y² + 4y + 4) - 3(y² + 2y) - 2y² - 2 = 0
( - y² + 4y + 2 - 3y² - 6y ) = 0
-4y² - 2y + 2 = 0
bagi dgn -2

2y² + y - 1 = 0
2y² + 2y - y - 1 = 0
2y(y + 1) - 1(y + 1) = 0
(2y - 1)(y + 1) = 0
y = 1/2 v y = -1

utk y = 1/2
x = y + 2
x = 1/2 +2
x= 5/2

utk y = -1
x = -1+2
x = 1

Hp
= { (5/2 , 1/2) , (1 , -1) }

System Equation.

x - y - 2 = 0
x - y = 2 → x = y + 2

Substitute x to x² - 3xy - 2y² - 2 = 0
(y + 2)² - 3(y + 2)y - 2y² - 2 = 0
y² + 4y + 4 - 3y² - 6y - 2y² - 2 = 0
-4y² - 2y + 2 = 0
2y² + y - 1 = 0
(2y² - y) + (2y - 1) = 0
y(2y - 1) + (2y - 1) = 0
(2y - 1)(y + 1) = 0
y = 1/2 or y = -1

For y = 1/2, x = 1/2 + 2 = 3/2
For y = -1, x = -1 + 2 = 1
HP = {(3/2, 1/2), (1, -1)}