Dik : 10x-5y+3z= -41, 8x+6y+5z = 18, 6x+3y+z= -13 .. Tentukan à.HP SPLTV, b.nilai x-y+z

jawab

(i) 10x - 5y + 3z = - 41
(ii) 8x + 6y + 5z= 18
(iii) 6x + 3y + z = -13

(i) dan (ii)
10x - 5y + 3z = - 41 } kali 5
8x + 6y + 5z = 18} kali 3

50x - 25y + 15 = - 205
24x + 18y + 15z = 54...(-)
26 x - 43 y = -259 ...(iv)

(i) dan (iii)
10x - 5y + 3z = - 41
6x + 3y + z = - 13} kali 3

10x - 5y + 3z  =- 41
18x + 9y + 3z = - 39 ...(-)
-8 x - 14y  = - 2} bagi -2
atau
4x + 7y =  1 ..(v)

(iv) dan (v)
26x  - 43 y  = - 259 } kali2
4x + 7y =  1 } kali 13
52 x - 86 y = - 518
52 x + 91 y = 13....(-)
- 177 y = -531
y = 3

4x + 7y = 1
4x + 21 =1
4x = - 20
x = - 5

10x - 5y + 3z  = -41
10(-5) - 5(3) + 3z = - 41
- 50 - 15 + 3z = - 41
3z= -41+ 65
z = 8

x- y + z = (-5) -(3) + 8 = -8+ 8
x - y + z = 0