no.1 tolong dibantu 3 variabenya 20 poin x+y+2z=1 4x+2y+z=4 9x+3y+z=17 no.2 a+b+2c=-6 2a-5b+c=-4 -3a-7b-3c=-13

Materi : SPLTV


x + y + 2z = 1 .....................(1)
4x + 2y + z = 4 .......................(2)
9x + 3y + z =17........................(3)

dari (1) dan (2)
x + y + 2z = 1
8x + 4y + 2z = 4
------------------------ (-)
7x + 3y = 3 .................................(4)

dari (2) dan (3)
4x + 2y + z = 4
9x + 3y + z =17
---------------------- (-)
5x + y = 13 ................................(5)

dari (4) dan (5)
7x + 3y = 3
15x + 3y = 39
----------------------(-)
6x = 36
x = 6

subtitusi x ke (4)
7x + 3y = 3
7(6) + 3y = 3
3y = 3 - 42
3y = 39
y = -13

subtitusi x dan y ke (1)
x + y + 2z = 1
6 - 13 + 2z = 1
2z = 1 + 7
2z = 8
z = 4

jadi HP : {(6,-13,4)}

=======================================================

a + b + 2c = -6 .............................(1)
2a - 5b + c= -4 ..............................(2)
-3a - 7b - 3c = -13 ........................(3)

dari (1) dan (2)
a + b + 2c = -6
4a - 10b + 2c= -8
------------------------- (-)
3a - 11b = -2 ................................(4)

dari (2) dan (3)
6a - 15b + 3c= -12
-3a - 7b - 3c = -13
-------------------------- (+)
3a - 22b = -25 ................................(5)

dari (4) dan (5)
6a - 22b = -4
3a - 22b = -25
---------------------- (-)
3a = 21
a = 7

subtitusi a ke (4)
3a - 11b = -2
3(7) - 11b = -2
11b = 21 + 2
b = 23/11

subtitusikan a dan b ke (1)
a + b + 2c = -6
7 + 23/11 + 2c = -6
2c = -66/11 - 77/11 - 23/11
c = -83/11

a.
x =>> -5
y =>> -4
z =>> 4

b.
x =>> 3
y =>> 2
z =>> - 12

c.
x =>> 2
y =>> 4
z =>> - 13