Kunci Jawaban Matematika Sukino Kelas X Peminatan Bab 2 LKS 3 Bagian B no 3d

3. Selesaikan sistem persamaan berikut. 

d.  

²log (4 + x - 5y) = 0

²log (x + 1) = 1 + 2 ²log y 

Jawaban :

²log (4 + x - 5y) = 0

²log (4 + x - 5y) = ²log 1

4 + x - 5y = 1

x - 5y = - 3 ... (i)

x = - 3 + 5y

²log (x + 1) = 1 + 2 ²log y

²log (x + 1) = ²log 2 + ²log y²

²log (x + 1) = ²log 2y²

x + 1 = 2y²

- 3 + 5y + 1 = 2y²

5y - 2 = 2y²

0 = 2y² - 5y + 2

0 = (2y - 1)(y - 2)

maka

2y - 1 = 0

2y = 1

y = 1/2

atau 

y - 2 = 0

y = 2

jika y = 1/2

maka 

x = - 3 + 5y

x = - 3 + 5 . 1/2

x = - 3 + 5/2

x =  - 1/2

jika y = 2

maka

x = - 3 + 5y

x = - 3 + 5 . 2

x = - 3 + 10

x = 7