Sistem persamaan linear 3 variabel 1. 2x - y = 5 3y + z = 0 x + 4z = 14 Tentukan himpunan penyelesaiannya 2. 2x + 3y - z = 5 x + y + z = 9 x - 2y - z = -7 Tentu

1) 2x - y = 5 => 2x = y + 5 => x = (y + 5)/2
2) 3y + z = 0 => z = -3y
3) x + 4z = 14
=> (y + 5)/2 + 4(-3y) = 14 ==> kedua ruas kali 2
=> y + 5 - 24y = 28
=> -23y = 23
=> y = -1
x = (y + 5)/2 = (-1 + 5)/2 = 4/2 = 2
z = -3y = -3(-1) = 3
HP = {(2, -1, 3)}


1) 2x + 3y - z = 5
2) x + y + z = 9
3) x - 2y - z = -7
Eliminasi 1) dan 2)
2x + 3y - z = 5
x + y + z = 9
-------------------- +
3x + 4y = 14 ....... (4)
Eliminasi 2) dan 3)
x + y + z = 9
x - 2y - z = -7
-------------------- +
2x - y = 2 ........... (5)
Eliminasi (4) dan (5)
3x + 4y = 14 |.1| 3x + 4y = 14
2x - y = 2 |. 4 | 8x - 4y = 8
--------------------------------------- +
............................ 11x = 22 => x = 2
(5) 2x - y = 2
=> 2(2) - y = 2
=> 4 - y = 2
=> y = 2
(2) x + y + z = 9
=> 2 + 2 + z = 9
=> z = 5
HP = {(2, 2, 5)}

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