Question

Diketahui sistem persamaan linear 3 variabel
x+2y-3z=4
2x-y+z=3
3x-3y+2z=3

Tentukan:
A) nilai X
B) nilai y
C) nilai z
D) y+z=-x
E) himpunan penyelesaian

Answer 1

X + 2y - 3z = 4 .....(1)
2x - y + z = 3 ......(2)
3x - 3y + 2z = 3 .......(3)

Eliminasi persamaan (1) dan (2) :
x + 2y - 3z = 4 |×2|
2x - y + z = 3 |×1|

2x + 4y - 6z = 8
2x - y + z = 3
...................................-
5y - 7z = 5 .......(4)

Eliminasi persamaan (1) dan (3) :
x + 2y - 3z = 4 |×3|
3x - 3y + 2z = 3 |×1|

3x + 6y - 9z = 12
3x - 3y + 2z = 3
....................................-
9y - 11z = 9 ........(5)

Eliminasi persamaan (4) dan (5) :
5y - 7z = 5 |×9|
9y - 11z = 9 |×5|

45y - 63z = 45
45y - 55z = 45
..................................-
-8z = 0
z = 0

Substitusi z kepersamaan (4) :
5y - 7z = 5
5y - 7(0) = 5
5y = 5
y = 1

Substitusi z dan y kepersamaan (1) :
x + 2y - 3z = 4
x + 2(1) - 3(0) = 4
x + 2 -0 = 4
x = 4 - 2
x = 2

Jadi :
A) Nilai x = 2
B) Nilai y = 1
C) Nilai z = 0
D) y + z = -x
1 + 0 = - 2
= -2 - 1 - 0
= -3
E) HP = {2, 1, 0}