Tentukan himpunan penyelesaian dari sistem persamaan linear dua variabel berikut dengan menggunakan metode gabungan, jika x, y ∈ R a. 2x + 5y = 8 dan x + 5y = 2

Bab SPLDV
Matematika SMP Kelas VIII

a]
2x + 5y = 8
...x + 5y = 2
----------------- -
x = 6

x + 5y = 2
6 + 5y = 2
5y = 2 - 6
y = -4/5

HP = { (6, -4/5) }

b]
y = 2x - 5
y = x + 3
-------------- -
0 = x - 8
x = 8

y = x + 3
y = 8 + 3
y = 11

HP = { (8, 11) }

c]
x = 2y - 3 → dikali 2 → 2x = 4y - 6

2x = 4y - 6 → 4y = 2x + 6

4y = 2x + 6
...y = 2x + 1
---------------- -
3y = 5
y = 5/3

y = 2x + 1
5/3 = 2x + 1
2x = 5/3 - 1
2x = 5/3 - 3/3
x = 2/3 : 2
x = 1/3

HP = { (1/3, 5/3) }