Question

Quiz

x + 4y - z = 1
-x + 2y + z = 2
2x + 6y + z = -8

_____
Eliminasinya (2 dan 3) & (1 dan 2) & (4 dan 5)​

Answer 1

Jawaban :

[tex]x + 4y - z = 1 \: \: \: \: \: (1) [/tex]

[tex] - x + 2y + z = 2 \: \: \: \: (2)[/tex]

[tex]2x + 6y + z = - 8 \: \: \: \: (3)[/tex]

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eliminasi (1) dan (2)

x + 4y - z = 1

-x + 2y + z = 2

__________ -

2x + 6y = -1 ..... (4)

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eliminasi (2) dan (3)

-x + 2y + z = 2

2x + 6y + z = -8

__________-

3x + 4y = -10 ..... (5)

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eliminasi (4) dan (5)

2x + 6y = -1 (×3) 6x + 18y = -3

3x + 4y = -10 (×2) 6x + 8y = -20

________________________-

10y = 17

y = 17/10

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2x + 6(17/10) = -1

2x + 102/10 = -1

2x + 51/5 = -1

2x = -1 - 51/5

2x = -56/5

x = -56/10

x = -28/5

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(-28/5) + 4(17/10) - z = 1

-56/10 + 68/10 - z = 1

12/10 - z = 1

6/5 - z = 1

6/5 - 1 = z

1/5 = z

z = 1/5

________

nilai dari

[tex]x = - \frac{ 28}{5} [/tex]

[tex]y = \frac{17}{10} [/tex]

[tex]z = \frac{1}{5} [/tex]

note : angkanya jelek banget :)

Answer 2

Jawaban:

[Persamaaan Linear 3 Variabel]

Penjelasan dengan langkah-langkah:

x+4y-z=1 ...(1)

-x+2y+z=2...(2)

2x+6y+z=-8 ...(3)

-x+2y+z=2...(2)

2x+6y+z=-8...(3) _

-3x-4y+0=10

-3x-4y=10....(4)

x+4y-z=1...(1)

-x+2y+z=2...(2) +

0+6y+0=3

6y =3 ...(5)

-3x-4y=10...(4) x 3

6y=3....(5) x 2

-9x-12y=30

12y=6 +

-9x+0=36

-9x=36

x=36/-9

x=-4

12y=6

y=6/12

y=1/2

x+4y-z=1

-4+4(1/2)-z=1

-4+2-z=1

-2-z=1

-z=1+2

-z=3

z=3/-1

z=-3

Maka:

x=-4, y=1/2, z=-3

Pembuktian:

x+4y-z=1

-4+4(1/2)-(-3)=1

-4+2+3=1

-2+3=1

1=1 (sama)

-x+2y+z=2

-(-4)+2(1/2)+(-3)=2

4+1-3=2

5-3=2

2=2 (sama)

2x+6y+z=-8

2(-4)+6(1/2)+(-3)=-8

-8+3-3=-8

-5-3=-8

-8=-8 (sama)

Demikian

Semoga membantu dan bermanfaat!