• Himpunan penyelesaian dari sistem persamaan linear tiga variabel adalah C. {(4,-7,2)}

PEMBAHASAN

DIKETAHUI

a + b + 2c = 1

4a + 2b + c = 4

9a + 3b + c = 17

DITANYA

HP = ?

JAWAB

Gunakan aturan substitusi

a + b + 2c = 1

a = 1 - 2c - b

4a + 2b + c = 4

4(1 - 2c - b) + 2b + c = 4

4 - 8c - 4b + 2b + c = 4

-7c - 2b = 4 - 4

-7c - 2b = 0

-2b = 7c

b = -7c/2

9a + 3b + c = 17

9(1 - 2c - b) + 3(-7c/2) + c = 17

9(1 - 2c + 7c/2) - 21c/2 + c = 17

9(1 + 3c/2) - 19c/2 = 17

9 + 27c/2 - 19c/2 = 17

(27c - 19c)/2 = 17 - 9

8c/2 = 8

4c = 8

c = 8/4

c = 2

b = -7c/2

b = -7.2/2

b = -14/2

b = -7

a = 1 - 2c - b

a = 1 - 2.2 - (-7)

a = 1 - 4 + 7

a = -3 + 7

a = 4

HP = {(4,-7,2)}