Diketahui:

• 3x - y + z = 11 .... pers 1
• 2x + y + z = 12 ... pers 2
• x + 2y - z = 3 .... pers 3

Ditanya:

HP

Penyelesaian:

eliminasi pers 1 dan pers 2

3x - y + z = 11

2x + y + z = 12

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

x - 2y = -1 .... pers 4

.

eliminasi pers 2 dan pers 3

2x + y + z = 12

x + 2y - z = 3

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

3x + 3y = 15

3(x + y) = 15

x + y = 15/3

x + y = 5 .... pers 5

.

eliminasi pers 4 dan pers 5

x - 2y = -1

x + y = 5

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

-3y = -6

y = -6/-3

y = 2

.

substitusi y ke pers 4

x - 2y = -1

x - 2(2) = -1

x - 4 = -1

x = -1 + 4

x = 3

.

substitusi x dan y ke pers 1

3x - y + z = 11

3(3) - 2 + z = 11

9 - 2 + z = 11

7 + z = 11

z = 11 - 7

z = 4

Maka:

HP = {x, y, z}

HP = {3, 2, 4}