Question

Tentukan nilai x,y dan z dari SPL 3 variabel berikut

1. 2x + 2y + z = 1400
x + y + 2z = 1300
x + 3y + z = 1500

Answer 1

2x + 2y + z = 1400 (i)
x + y + 2z = 1300 (ii)
x + 3y + z = 1500 (iii)

eliminasi pers (ii) dan (iii)
x + y + 2z = 1300 (ii)
x + 3y + z = 1500 (iii)
----------------------------- -
-2y + z = -200 (iv)

eliminasi pers (i) dan (ii)
2x + 2y + z = 1400 (i) dikali 1
x + y + 2z = 1300 (ii) dikali 2

2x + 2y + z = 1400
2x + 2y + 4z = 2600
------------------------------- -
-3z = -1200
z = 400

substitikan z dengan pers (iv)
-2y + z = -200 (iv)
-2y + 400 = -200
-2y = -200 - 400
-2y = -600
y = -600/-2
y = 300

2x + 2y + z = 1400 (i)
2x + 2(300) + 400 = 1400
2x + 600 + 400 = 1400
2x + 1000 = 1400
2x = 1400 - 1000
2x = 400
x = 400/2
x = 200

jadi
x = 200
y = 300
z = 400