Carilah himpunan penyelesaian dari spltv berikut dengan cara gabungan

x = 1, y = 1, z = –1

Penjelasan dengan langkah-langkah:

2x + 3y – z = 6 ….. (1)

4x + 2y + 3z = 3 ….. (2)

3x – y – 2z = 4 ….. (3)

metode eliminasi:

2x + 3y – z = 6 |×2| 4x + 6y – 2z = 12

4x + 2y + 3z = 3 |×1| 4x + 2y + 3z = 3

_____________-

4y – 5z = 9

2x + 3y – z = 6 |×3| 6x + 9y – 3z = 18

3x – y – 2z = 4 |×2| 6x – 2y – 4z = 8

_____________-

11y + z = 10

4y – 5z = 9 |×11| 44y – 55z = 99

11y + z = 10 |×4| 44y + 4z = 40

____________-

-59z = 59

z = -1

metode substitusi:

4y – 5z = 9

4y – 5(-1) = 9

4y + 5 = 9

4y = 9 – 5

4y = 4

y = 1

2x + 3y – z = 6

2x + 3(1) – (-1) = 6

2x + 3 + 1 = 6

2x + 4 = 6

2x = 6 – 4

2x = 2

x = 1