Question

Himpunan penyelesaian dari 10/x - 4/y = 4 dan 4/x + 8/y = 4 adalah...

a. (-4,-4)
b. (6,4)
c. (4,6)
d. (2,4)

(Tolong jawab pakai cara)

Answer 1

10/x - 4/y = 4
(10y-4x)/xy = 4
10y-4x=4xy
 -4x + 10y = 4xy (dibagi 2)
-2x + 5y = 2xy 
2x+2xy=5y
2(x+y)=5y
y=2(x+y)/5 (i)   

4/x + 8/y = 4 
(4y+8x)/xy = 4
4y+8x = 4xy
 8x + 4y = 8xy   (dibagi 4)
2x + y = 2xy
2x-2xy = -y
2(x-y)=-y
y=-2(x-y)
y=2(y-x)....(ii)

per (i) dan (ii) di subst
2(x+y)/5 = 2(y-x)
x+y=5(y-x)
x+y=5y-5x
x=2y/3 .. di subs ke pers (ii) y=2(y-x)---.>y=2(y - 2y/3)--> y = 2(y/3)