Question

Penyelesaian dari sistem persamaan
3x - y + 2xy = 0
5x + 3y + xy = 0
adalah...

Answer 1

3x - y + 2xy = 0 ...sederhakan dengan dibagi (xy)
3/y - 1/x + 2 = 0
-1/x + 3/y = - 2  ....(1)

5x+ 3y + xy = 0  bagikan dengan (xy)
5/y + 3/x + 1 = 0
3/x + 5/y = -1  ......(2)

misal 1/x = a dn 1/y = b
pers 1 --> -1/x + 3/y = -2 --> -a + 3b = - 2 
pers 2--> 3/x + 5/y = -1  --> 3a + 5b = -1
eliminasi
-a + 3b = - 2 .....(kalikan 3)
3a + 5b = -1
.
-3a + 9b = - 6
3a + 5b = -1
------------------(+)
14 b  = - 7
b = -7/14
b = - 1/2  --> y = - 2 

-a + 3b = - 2
-a = - 2 - 3b
a = 2 + 3b
a = 2 + 3(-1/2)
a = 2 - 3/2
a = 1/2  ----> x = 2
.
hp (x,y)= (2, -2)