Question

Tentukan himpunan penyelesaian dari sistem persamaan berikut .

1.x+y+z=0
2x+y-z=7
x+2y+3z=-4

2.2x-y+2z=-3
x+2y-5z=-7
5x-4y-z=-33

3.x+y-2z=-1
3x+y-2z=17
2x-2y-z=8

yang bisa jawab dengan benar ..nanti aku kasih jawaban terbaik..

Answer 1

Verified answer

1.
x + y + z = 0
2x + y - z = 7
x + 2y + 3z = - 4

x + y + z = 0
x = - y - z

x + 2y + 3z = - 4
- y - z + 2y + 3z = - 4
y + 2z = - 4

2x + y - z = 7
2(- y - z) + y - z = 7
- 2y - 2z + y - z = 7
- y - 3z = 7

y + 2z = - 4|× 3
- y - 3z = 7|× 2

3y + 6z = - 12
- 2y - 6z = 14
__________+
y = 2

y + 2z = - 4
2 + 2z = - 4
2z = - 4 - 2
2z = - 6
z = - 3

x = - y - z
x = - 2 + 3
x = 1

2.
2x - y + 2z = - 3
x + 2y - 5z = - 7
5x - 4y - z = - 33

x + 2y - 5z = - 7
x = - 7 - 2y + 5z
x = 5z - 2y - 7

2x - y + 2z = - 3
2(5z - 2y - 7) - y + 2z = - 3
10z - 4y - 14 - y + 2z = - 3
12z - 5y = - 3 + 14
12z - 5y = 11

5x - 4y - z = - 33
5(5z - 2y - 7) - 4y - z = - 33
25z - 10y - 35 - 4y - z = - 33
24z - 14y = - 33 + 35
24z - 14y = 2

24z - 14y = 2|× 1
12z - 5y = 11|× 2

24z - 14y = 2
24z - 10y = 22
___________—
- 4y = - 20
y = 5

12z - 5y = 11
12z - 25 = 11
12z = 11 + 25
12z = 36
z = 3

x = 5z - 2y - 7
x = 15 - 10 - 7
x = - 2

3.
x + y - 2z = - 1
3x + y - 2z = 17
2x - 2y - z = 8

x + y - 2z = - 1
x = - 1 - y + 2z

2x - 2y - z = 8
2(- 1 - y + 2z) - 2y - z = 8
- 2 - 2y + 4z - 2y - z = 8
- 4y + 3z = 8 + 2
- 4y + 3z = 10

3x + y - 2z = 17
3(- 1 - y + 2z) + y - 2z = 17
- 3 - 3y + 6z + y - 2z = 17
- 2y + 4z = 17 + 3
- 2y + 4z = 20

- 4y + 3z = 6|× 1
- 2y + 4z = 20|× 2

- 4y + 3z = 10
- 4y + 8z = 40
___________—
- 5z = - 30
z = 6

- 2y + 4z = 20
- 2y + 24 = 20
- 2y = 20 - 24
- 2y = - 4
y = 2

x = - 1 - y + 2z
x = - 1 - 2 + 12
x = 9

Maaf Kalau Salah