Ambil persamaan (1) dan (2)

Eliminasi y

3x + 4y + 5z = 3 | ×1 | 3x + 4y + 5z = 3

x - y + 7z = 12 | ×4 | 4x - 4y + 28z = 48

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

7x + 33z = 51......(4)

Ambil persamaan (1) dan (3)

3x + 4y + 5z = 3

4x + 4y + 7z = 6

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

-x - 2z = -3.......(5)

Didapat persamaan (4) dan (5)

7x + 33z = 51

-x - 2z = -3

Eliminasi x

7x + 33z = 51 | ×1 | 7x + 33z = 51

-x - 2z = -3 | ×7 | -7x - 14z = -21

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

19z = 30

z = 30/19

Substitusi z = 30/19 pada persamaan (5)

-x - 2z = -3

-x - 2( 30/19 ) = -3

-x - 60/19 = -3

-60/19 + 3 = x

-60/19 + 57/19 = x

x = -3/19

Substitusi x = -3/19 dan z = 30/19 pada persamaan (2)

x - y + 7z = 12

-3/19 - y + 7( 30/19 ) = 12

-3/19 + y + 210/19 = 12

207/19 + y = 12

y = 12 - 207/19

y = 228/19 - 207/19

y = 21/19

HP = { ( -3/19, 21/19, 30/19 ) }