Question

2x+y =4
x^2 + y^2 =5
tentukan hp

Answer 1

2x + y = 4
y = 4-2x

x^2 + y^2 = 5
x^2 + (4-2x)^2 = 5
x^2 + 16 - 16x + 4x^2 = 5
5x^2 -16x + 16 - 5 = 0
5x^2 -16x + 11 = 0
(x - 1)(5x - 11) = 0
maka ,,,
x - 1 = 0
x = 1

5x -11 =0
5x = 11
x = 11/5

substitusikan ke y= 4-2x
maka jika x = 1
y = 4 - 2(1) = 4-2 = 2
(1,2)

jika x = 11/5 maka,,
y = 4-2(11/5) = 4 - 22/5 = 20/5 - 22/5 = -2/5
(11/5 , -2/5)

maka HP = { (11/5 , -2/5) , (1 , 2) }