Question

Tentukan himpunan penyelesaian dari :
x + y + z = -1
x + 2y + 3z = 5
3x - 2y - z = -9

Answer 1

SPLTV

(1) x + y + z = -1

(2) x + 2y + 3z = 5

(3) 3x - 2y - z = -9

Eliminasi z

(1) + (3)

4x - y = -10 ... (4)

x + y + z = -1 || × 3

3x + 3y + 3z = -3

x + 2y + 3z = 5

Kurangkan

2x + y = -8 ... (5)

4x - y = -10

2x + y = -8

Jumlahkan

6x = -18

x = -3 ✔

4x - y = -10

y = 4x + 10

y = -12 + 10

y = -2 ✔

x + y + z = -1

-3 + (-2) + z = -1

z = 4 ✔

(x,y,z) = (-3,-2,4)

Answer 2

Eliminasi y
pers. 2&3
x+2y+3z=5
3x-2y-z=-9
_________+
4x+2z=-4 > pers. 4

eliminasi 1&3
x+y+z=-1 | x2
3x-2y-z=-9

2x+2y+2z=-2
3x-2y-z=-9
__________+
5x+z=-11 > pers. 5

SPLDV pers. 4&5
4x+2z=-4
5x+z=-11 |x2

4x+2z=-4
10x+2z=-22
_________-
-6x= 18
x= -3
sub. ke pers. 4
4x+2z=-4
-12+2z=-4
2z=8
z=4

sub. x&z ke pers. 1
x+y+z=-1
-3+y+4=-1
y=-2

HP (-3,-2,4) > x,y,z