Question

BIG POINT (50 POINT)

x + 2y = 12 ... (1)
3y + 3z = 9 ... (2)
2x + y + 2z = 16 ... (3)
Tentukan HP!!​

Answer 1

HP = { (x, y, z) | (32/5, 14/5, 1/5) }
 

Penjelasan dengan langkah-langkah

Diberikan SPLTV:

• x + 2y = 12   ...(1)
• 3y + 3z = 9   ...(2)
• 2x + y + 2z = 16   ...(3)

Penyelesaian SPLTV

Persamaan (2) ekuivalen dengan:
y + z = 3
⇔ y = 3 – z   ...(4)

Substitusi (4) → (1):
x + 2(3 – z) = 12
⇔ x + 6 – 2z = 12
⇔ x – 2z = 6
⇔ x = 2z + 6   ...(5)

Substitusi (4), (5) → (3).
2(2z + 6) + (3 – z) + 2z = 16
⇔ 4z + 12 + 3 – z + 2z = 16
⇔ 5z + 15 = 16
⇔ 5z = 1
⇔ z = 1/5.

Substitusi nilai z → (4).
y = 3 – 1/5
⇔ y = 14/5.

Substitusi nilai z → (5).
x = 2(1/5) + 6 = 2/5 + 6
⇔ x = 32/5.

∴ HP = { (x, y, z) | (32/5, 14/5, 1/5) }

Answer 2

Verified answer

Jawaban:

HP {x, y z} = {32/5, 14/5, 1/5}

Penjelasan dengan langkah-langkah:

x + 2y = 12 ... (1)

3y + 3z = 9 ... (2)

2x + y + 2z = 16 ... (3)

..

x + 2y = 12

x = 12 - 2y ... (4)

..

3y + 3z = 9

3y + z = 3

z = 3 - y ... (5)

..

Sub (4) dan (5) → (3)

2x + y + 2z = 16

2(12 - 2y) + y + 2(3 - y) = 16

24 - 4y + y + 6 - y = 16

5y = 14

y = 2,8 ... (Y)

..

Sub (Y) → (1)

x + 2y = 12

x + 2(2,8) = 12

x + 5,6 = 12

x = 6,4 ... (X)

..

Sub (Y) → (2)

3y + 3z = 9

3(2,8) + 3z = 9

8,4 + 3z = 9

3z = 0,6

z = 0,2

..

x = 6,4 = 6 + 2/5 = 32/5

y = 2,8 = 2 + 4/5 = 14/5

z = 0,2 = 1/5

[tex]\boxed{\colorbox{ccddff}{Answered by Danial Alf'at}}[/tex]