Jawab:

Penjelasan dengan langkah-langkah:

x1 – x2 + x3 –2x4 = 8

2x1 – x2 + 2x3 – x4 = 5

-x1 + x2 + 2x3 – x4 = 4

x1 + 2x2 + 4x3 + x4 = 5

Misal :

x1 = p, x2 = q, x3 = r, x4 = s

p – q + r –2s = 8

2p – q + 2r – s = 5

-p + q + 2r – s = 4

p + 2q + 4r + s = 5

p = 8 + q - r + 2s

2 (8 + q - r + 2s) - q + 2r - s = 5

16 + 2q - 2r + 4s - q + 2r - s = 5

q + 3s = 5 - 16

q + 3s = -11

q = -11 - 3s

-(8 + q - r + 2s) + (-11 - 3s) + 2r – s = 4

-8 - q + r - 2s - 11 - 3s + 2r - s = 4

-8 - (-11 - 3s) + r - 2s - 11 - 3s + 2r - s = 4

-8 + 11 + 3s + r - 2s - 11 - 3s + 2r - s = 4

-3s + 3r = 4 + 8 - 11 + 11

-3s + 3r = 12

-s + r = 4

r = 4 + s

8 + (-11 - 3s) - (4 + s) + 2s + 2(-11 - 3s) + 4(4 + s) + s = 5

8 - 11 - 3s - 4 - s + 2s - 22 - 6s + 16 + 4s + s = 5

(-3 - 1 + 2 - 6 + 4 + 1)s = 5 - 8 + 11 + 4 + 22 - 16

-3s = 18

s = 18/(-3) = -6

r = 4 + (-6) = -2

q = -11 - 3(-6) = -11 + 18 = 7

p = 8 + 7 - (-2) + 2(-6) = 8 + 7 + 2 - 12 = 5

Jadi, x1 = 5, x2 = 7, x3 = -2 dan x4 = -6