Page 24 - 1W. MODUL SPLDTV DAN KUADRAT_Neat

02. Dengan metoda campuran, tentukanlah penyelesaian sistem persamaan linier :
2x + y + 3z = 1
2x – 3y + 4z = –5
x + 2y – z = 7
Jawab
Misalkan : 2x + y + 3z = 1 ............................................................................ (1)
2x – 3y + 4z = –5 ......................................................................... (2)
x + 2y – z = 7 .......................................................................... (3)

(1)(2) 2x + y + 3z = 1
2x – 3y + 4z = –5

4y – z = 6 ................................................................................... (4)

(1)(3) 2x + y + 3z = 1 (1) 2x + y + 3z = 1
x + 2y – z = 7 (2) 2x + 4y – 2z = 14

–3y = 3 –3y + 5z = –13 .............................. (5)

(4)(5) 4y – z = 6 (5) 20y – 5z = 30
–3y + 5z = –13 (1) –3y + 5z = –13

–8 – 7z = –22 17y = 17
y = 1.............................................. (6)

(4)(6) 4y – z = 6
4(1) – z = 6
4 – z = 6
4 – 6 = z
z = –2 .................................................................................................... (7)

(1)(6)(7) 2x + y + 3z = 1
2x + (1) + 3(–2) = 1
2x + 1 – 6 = 1
2x – 5 = 1
2x = 6
x = 3
Jadi himpunan penyelesaiannya H = {(3, 1, –2)}

03. Dengan metoda campuran, tentukanlah penyelesaian sistem persamaan linier :
2x + 3y – 3z = 10
2x – y + 2z = 1
4x + 4y + z = 11
Jawab
Misalkan : 2x + 3y – 3z = 10 ......................................................................... (1)
2x – y + 2z = 1 ............................................................................ (2)
4x + 4y + z = 11 ........................................................................ (3)

Sistem Persamaan Linier 2