Diberikan persamaan sbb:
2w - x + 5y + z = -3
3w + 2x + 2y - 6z = -32
w + 3x + 3y - z = -47
5w - 2x - 3y + 3z = 49
Maka nilai w + x + y + z adalah...
Wajib disertakan nama bab/materi nya ya... Thx
2w - x + 5y + z = -3
3w + 2x + 2y - 6z = -32
w + 3x + 3y - z = -47
5w - 2x - 3y + 3z = 49
Maka nilai w + x + y + z adalah...
Wajib disertakan nama bab/materi nya ya... Thx
Verified answer
Persamaan Linear 4 Variabel2w - x + 5y + z = -3 ............ (1)
3w + 2x + 2y - 6z = -32 .............(2)
w + 3x + 3y - z = -47 .............(3)
5w - 2x - 3y + 3z = 49 .............(4)
Eliminasi 1 dan 2
2w - x + 5y + z = -3 |x2| 4w - 2x + 10y + 2z = -6
3w + 2x + 2y - 6z = -32 |x1| 3w + 2x + 2y - 6z = -32
------------------------------- + -------------------------------- +
7w + 12y - 4z = -38 ...... (5)
Eliminasi 2 dan 3
3w + 2x + 2y - 6z = -32 |x3| 9w + 6x + 6y - 18z = -96
w + 3x + 3y - z = -47 |x2| 2w + 6x + 6y - 2z = -94
------------------------------- - -------------------------------- -
7w - 16z = -2 ...... (6)
Eliminasi 2 dan 4
3w + 2x + 2y - 6z = -32
5w - 2x - 3y + 3z = 49
------------------------------- +
8w - y - 3z = 17 .......... (7)
Eliminasi 7 dan 5
8w - y - 3z = 17 |x12| 96w - 12y - 36z = 204
7w + 12y - 4z = -38 |x1| 7w + 12y - 4z = -38
-------------------------- + ----------------------------- +
103w - 40z = 166 ......... (8)
Eliminasi 6 dan 8
7w - 16z = -2 |x103| 721w - 1648z = -206
103w - 40z = 166 |x7| 721w - 280z = 1162
----------------------- - ------------------------- -
-1368z = -1368
z = 1
Subtitusikan ke pers (6)
7w - 16z = -2
7w - 16 (1) = -2
7w - 16 = -2
7w = 14
w = 2
Subtitusikan ke pers (7)
8w - y - 3z = 17
8 (2) - y - 3 (1) = 17
16 - y - 3 = 17
-y + 13 = 17
-y = 4
y = -4
Subtitusikan ke pers (1)
2w - x + 5y + z = -3
2 (2) - x + 5 (-4) + 1 = -3
4 - x + (-20) + 1 = -3
-x - 15 = -3
-x = 12
x = -12
Maka nilai w + x + y + z adalah||
= w + x + y + z
= 2 + (-12) + (-4) + 1
= -13 ✔️
Semoga Membantu!!!
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