Tentukan himpunan penyelesaian dari sistem persamaan linear dua variabel berikut dengan menggunakan metode gabungan, jika x, y ∈ R. a. 5x - y = 3 dan 10x - 5y =

SPLDV

Metode GABUNGAN

a.
5x - y = 3 ---> y = 5x - 3
10x - 5y = 15 || : 5
2x - y = 3
Eliminasi y
5x - y = 3
2x - y = 3
-------------- (-)
3x = 0
x = 0

substitusi x = 0 ke y = 5x - 3
y = 5.0 - 3
y = -3

HP = {(0,-3)}

b.
x + 4y = 8 || × 2
2x + 8y = 16

2x - y = 3 --> y = 2x - 3

Eliminasi x
2x + 8y = 16
2x - y = 3
----------------- (-)
9y = 13
y = 13/9

substitusi
y = 2x - 3
13/9 = 2x - 3
2x = 13/9 + 27/9
2x = 40/9
x = 20/9

HP = {(20/9 , 13/9)}

Kelas 8 Matematika
Bab 4 - SPLDV

a] 10x - 5y = 15 → dibagi 5 → 2x - y = 3

5x - y = 3
2x - y = 3
-------------- -
3x = 0
x = 0

5x - y = 3
5 . 0 - y = 3
-y = 3
y = -3

HP = { (0, -3) }

b] 2x - y = 3 → dikali 4 → 8x - 4y = 12

8x - 4y = 12
..x + 4y = 8
-------------------- +
9x = 20
x = 20/9

x + 4y = 8
20/9 + 4y = 8
4y = 72/9 - 20/9
y = 52/9 : 4
y = 13/9

HP = { (20/9, 13/9) }