Persamaan linear 3 variabel...!!!
Tentukan HP dari:
3x + y - z = 6 .............(1)
2x - 3y + z = 11 .............(2)
x - y + 3z = 10 .............(3)
Tentukan HP dari:
3x + y - z = 6 .............(1)
2x - 3y + z = 11 .............(2)
x - y + 3z = 10 .............(3)
Dg metode subsitusi
3x + y -z = 6
y = 6+z-3x
subsitusikan ke 2x -3y +z = 11
2x - 3(6+z-3x) + z = 11
2x -18 - 3z + 9x +z = 11
11x -2z = 29
subsitusikan ke x - y + 3z = 10
x - (6+z-3x) + 3z = 10
x - 6 -z + 3x + 3z = 10
4x + 2z = 16
eliminasikan
11x - 2z = 29
4x + 2z = 16
---------------- +
15x = 45
x = 45/15
= 3
subsitusikan ke 4x + 2z = 16
4(3) + 2z = 16
12 + 2z = 16
2z = 16-12
2z = 4
z = 4/2
= 2
y = 6 + z -3x
= 6 + 2 -3(3)
= 6 + 2 - 9
= -1
hp = { 3, -1, 2}
3x + y -z = 6
y = 6+z-3x
subsitusikan ke 2x -3y +z = 11
2x - 3(6+z-3x) + z = 11
2x -18 - 3z + 9x +z = 11
11x -2z = 29
subsitusikan ke x - y + 3z = 10
x - (6+z-3x) + 3z = 10
x - 6 -z + 3x + 3z = 10
4x + 2z = 16
eliminasikan
11x - 2z = 29
4x + 2z = 16
---------------- +
15x = 45
x = 45/15
= 3
subsitusikan ke 4x + 2z = 16
4(3) + 2z = 16
12 + 2z = 16
2z = 16-12
2z = 4
z = 4/2
= 2
y = 6 + z -3x
= 6 + 2 -3(3)
= 6 + 2 - 9
= -1
hp = { 3, -1, 2}
2 votes
Thanks 1
2x - 3y + z = 11 ......... (2)
x - y + 3z = 10 ............(3)
Kita eliminasi z dulu
Dari persamaan (1) dan (2)
3x + y - z = 6
2x - 3y + z = 11
_______________ +
5x - 2y = 17. . . . . . . . . (4)
Dari persamaan (1) dan (3)
3x + y - z = 6 → X3 → 9x + 3y - 3z = 18
x - y + 3z = 10 → X1 → x - y + 3z = 10
_______________ +
10x + 2y = 28. . . . . (5)
Eliminasi y dari persamaan (4) dan (5)
5x - 2y = 17
10x + 2y = 28
____________ +
15x = 45
x = 45/15
x = 3
Substitusi nilai x ke persamaan (5)
10x + 2y = 28
10(3) + 2y = 28
30 + 2y = 28
2y = 28 - 30
2y = -2
y = -1
Substitusi nilai x dan y ke persamaan (1)
3x + y - z = 6
3(3) - 1 - z = 6
9 - 1 - z = 6
8 - 6 = z
z = 2
Jadi, HP nya adalah {x, y, z} = {3, -1, 2)