Matematika " Eliminasi Hp "

Contoh soal mengenai Eliminasi

No. 1

3x – y + 4z = 8.... (1)

5x + y + 2z =12.... (2)

2x + 2y + 3z =14.... (3)

eliminasi (1) dan (2) => hilangkan variabel y

1. 3x – y + 4z = 8
2. 5x + y + 2z = 12+

8x + 6z = 20.... (4)

eliminasi (1) dan (3) => hilangkan variabel y

1. 3x – y + 4z = 8 . 2 =>6x – 2y + 8z = 16
2. 2x + 2y + 3z = 14 . 1 =>2x + 2y + 3z = 14

8x + 11z = 30.... (5)

eliminasi (4) dan (5) => hilangkan variabel x

4. 8x + 6z = 20
5. 8x + 11z = 30 +
   5z = -10

                   z = 2

subsitusi z = 2 ke (4)

8x + 6z = 20

8x + 6(2) = 20

8x + 12= 20

8x = 20 – 12

8x = 8

x = 1

subsitusi x= 1 dan z = 2 ke (1)

3x – y + 4z = 8

3(1) – y + 4(2) = 8

3 – y + 8 = 8

11 – y = 8

-y = 8 – 11

-y = -3

y = 3

Jadi, Hp = { 1, 3, 2 }