Tentukan himpunan penyelesaian dari sistem persamaan : [tex] 5x = 12 + 3y \\\\ \dfrac{3x}{y} - \dfrac{2y}{x} = 1 [/tex]

Gunakan Metode Subtitusi

5x = 12 + 3y
x = (12 + 3y)/5

3x/y - 2y/x = 1
(3x² - 2y²) / xy = 1
3x² - 2y² = xy
3(12 + 3y)²/5 - 2y² = (12 + 3y)/5 . y

masing² dikali 5
3(12 + 3y)² - 10y² = 12y + 3y²
3(144 + 72x + 9y²) - 10y² = 12y + 3y²
432 + 216x + 27y² - 10y² = 12y + 3y²
14y² + 204y + 432 = 0

masing² dibagi 2
7y² + 102y + 216 = 0
(7y + 18)(y + 12) = 0
y = -18/7 dan y = -12

x = (12 + 3y) / 5
x = (12 + 3.(-18/7) / 5
x = (12 - 54/7) / 5
x = (84/7 - 54/7) × 1/5
x = 30/7 × 1/5
x = 6/7

x = (12 + 3y) / 5
x = (12 + 3.(-12) / 5
x = (12 - 36) / 5
x = -24/5

maka
HP {6/7 , -18/7}

semoga berguna +_+

Semoga berguna +_+

Misal :
a = x/y

3x/y - 2y/x = 1
3a - 2/a = 1
3a² - a - 2 = 0
(3a + 2)(a - 1) = 0
a = -2/3 atau a = 1

▶ Utk x/y = -2/3
x = -2/3 y
5x = 12 + 3y
-10/3 y = 12 + 3y
-19/3 y = 12
y = -36/19 ---> x = -2/3 . -36/19 = 24/19

▶ utk x/y = 1
x = y
5x = 12 + 3y
2y = 12
y = 6 --> x = y = 6



HP = {(24/19 , -36/19) , (6 , 6)}