Page 38 - Buku Siap OSN Matematika SMP 2015(1)

Aljabar

Soal dan Pembahasan

1. Jika diketahui sistem persamaan linear dua variabel 1234567x + 7654321y =
3456789 dan 7654321x + 1234567y = 9876543. Bagaimana cara menentukan
2
2
nilai x – y ?
Jawab:
1234567x + 7654321y = 3456789

7654321x + 1234567y = 9876543 +

(1234567 + 7654321)x + (1234567 + 7654321)y = 3456789 + 9876543

(7654321 + 1234567)  (x + y) = 3456789 + 9876543


3456789 9876543 13333332
x + y = =

1234567 7654321 8888888
1234567x + 7654321y = 3456789
7654321x + 1234567y = 9876543 –

(1234567 – 7654321)x + (7654321 – 1234567)y = 3456789 + 9876543

(1234567 – 7654321)  (x – y) = 3456789 – 9876543

3456789 9876543 6419754
x – y = = = 1

1234567 7654321 6419754
Sehingga:
2
2
x – y = (x + y)(x – y)
13333332
= 1 
8888888

13333332
=
8888888


3 4444444 3
= =

2 4444444 2
3
2
2
Jadi, x – y =
2

Siap OSN Matematika SMP 2015 29