Himpunan penyelesaian sistem persamaan {x² - xy - y², = 0 2x - y - 1 = 0 }

jawab
x² - xy - y² = 0 ...(i)
2x - y - 1 = 0  atau y = 2x - 1 substitusi ke (i)

x² - x(y) - (y)² =0
x² - x(2x-1) -(2x-1)² = 0
x² - 2x² + x - (4x² -4x +1) = 0
x² -2x² + x - 4x² + 4x - 1 = 0
-5x² + 5x - 1= 0
x² - x + 1/5 =0
x² - x = - 1/5
(x -1/2)² = -1/5 + 1/4 = 1/20
x - 1/2 = √(1/20)= +_ 1/10 √5
x1 = 1/2 + 1/10 √5
x2 = 1/2 - 1/10 √5

y1 = 2x1 -1  = 1 + 1/5 √5  - 1 = 1/5 √5
y2= 2x2 - 1 = 1 - 1/5 √5 -1 =  - 1/5 √5

(x1,y1), (x2,y2) = (1/2 +1/10√5 , 1/5 √5) , (1/2 - 1/10√5 , -1/5 √5)

2x-y-1=0
y=2x-1

x^2-x(2x-1)-(2x-1)^2=0
x^2-2x^2+x-(4x^2-4x+1)=0
-x^2+x-(4x^2-4x+1)=0
-5x^2+5x-1=0
5x^2-5x+1=0
x1=((5)+(25-4*5*1))/10
x1=0,724
x2=((5)-(25-4*5*1))/10
x2=0,276
y1=2(0,724)-1=0,448
y2=2(0,276)-1=-0,448

(x1,y1)=(0,724 , 0,448)
(x2,y2)=(0,276 , -0,448)