jika 1/x + y = 6 dan 1/y + x = 2/3 dengan x, y, > 0, maka.... buatkan caranya yaa thanks

jawab
1/x + y = 6
1/x = 6 - y

1/y + x = 2/3
x = 2/3 - 1/y
x = (2y - 3)/3y
1/x= 3y/(2y - 3)

6 - y =  3y / (2y -3)
3y = (6 - y)(2y - 3)
3y = 12y - 18 - 2y² + 3y
3y = -2y² + 15y - 18
2y² - 12y + 18 = 0
y² - 6y + 9= 0
(y - 3)² = 0
y = 3

1/x = 6- y
1/x = 6 - 3 = 3
x = 1/3