Question

Himpunan penyelesaian dari sistem persamaan linear tiga variabel berikut adalah
2x + 2y + 3z = 14
3x – y + 4z = 8
5x + y + 2z = 12

Answer 1

Penjelasan dengan langkah-langkah:

2x + 2y + 3z = 14 (×1)

3x - y + 4z = 8 (×2)

------------------------------

2x + 2y + 3z = 14

6x - 2y + 8z = 16

------------------------------ +

8x + 11z = 30

3x - y + 4z = 8

5x + y + 2z = 12

----------------------- +

8x + 6z = 20

8x + 11z = 30

8x + 6z = 20

------------------ -

5z = 10

z = 10/5 = 2

8x + 6z = 20

8x + 6(2) = 20

8x + 12 = 20

8x = 20 - 12

8x = 8

x = 8/8 = 1

3x - y + 4z = 8

3(1) - y + 4(2) = 8

3 - y + 8 = 8

11 - y = 8

y = 11 - 8

y = 3

Himpunan Penyelesaian = {x, y, z} = {1, 3, 2}