Nama : Prima Ditya H
NIM : 2502163392
Jurusan : Teknik Industri
SOAL SPL PEMANTAPAN
Tentukan solusi sistem persamaan linier (SPL) berikut jika ada
a. X – 2Y + Z = 4
b. X + 2Y – Z = 2
c. -2P – 3Q + 2R = 3
-2X + Y -3Z = -6
-2X + Y + Z = 2
3P + 2Q - R = 2
3X – 3Y + Z = 7
- X – 2Y + Z = -2
2P + 3Q – 2R = 4
Jawab
a.
Memakai metode Eleminasi
X – 2Y + Z = 4
−2X + 4Y − 2Z = −8
−2X + Y − 3Z = −6
−2X + Y − 3Z
3X – 3Y + Z = 7
= −6 −
3Y + Z = −2
X – 2Y + Z = 4
3X – 6Y + 3Z = 12
3X – 3Y + Z = 7
3X − 3Y + Z = 7 –
−3Y + 2Z = 5
3Y + Z
= −2
−3Y + 2Z = 5 +
3Z = 3
𝐙 = 𝟏
3Y + Z = −2
X – 2Y + Z = 4
3Y + 1 = −2
X+2 + 1 = 4
3Y = −3Y
𝐘 = −𝟏
Maka nilai X = 1, Y = -1 dan Z = 1
X + 2 + 1 = 4
𝐗 = 𝟏
B.
X + 2Y – Z = 2
X + 2Y – Z = 2
−2X + Y + Z = 2
−X − 2Y + Z = −2 +
− X – 2Y + Z = −2
hasilnya 0 persamaan tidak ada solusi
C.
−2P – 3Q + 2R = 3
−2P – 3Q + 2R = 3
3P + 2Q − R = 2
2P + 3Q – 2R = 4 +
2P + 3Q – 2R
= 4
hasilnya 0 persamaan tidak ada solusi