2x-5y+z=14 X+4y-2z=-6 2x-y+z=6 Carilah harga x, y, z dengan ; a. Metode eliminasi b. Substitusi c. Campuran

a)
2x - 5y + z = 14 (× 4)
x + 4y - 2z = -6 (× 5)

8x - 20y + ..4z =. 56
5x + 20y - 10z = -30
----------------------------- +
13x - 6z = 26 (1)

2x - 5y + z = 14 (× 1)
2x - y + z = 6 (× 5)

.2x - 5y + ..z = 14
10x - 5y + 5z = 30
--------------------------- -
-8x - 4z = -16 (2)

(1) 13x - 6z = 26 (× 2)
(2) -8x - 4z = -16 (× 3)

26x - 12z =.. 52
-24x - 12z = -48
------------------------ -
50x = 100
x = 100/50
x = 2

(1) 13x - 6z = 26 (× 8)
(2) -8x - 4z = -16 (× 13)

.104x - 48z = .208
-104x - 52z = -208
---------------------------- +
-100z = 0
z = 0/-100
z = 0

2x - 5y + z = 14
2x -....y + z = ..6
------------------------ -
-4y = 8
y = 8/-4
y = -2

Jadi nilai x , y , dan z adalah {2 , -2 , 0}
b)
2x - 5y + z = 14
5y = 2x + z - 14
y = (2x + z - 14)/5

x + 4y - 2z = -6
x + 4(2x + z - 14)/5 - 2z = -6
5x/5 + (8x + 4z - 56)/5 - 10z/5 = -6
(5x + 8x + 4z - 56 - 10z)/5 = -6
13x - 6z - 56 = -6 × 5
13x - 6z - 56 = -30
13x - 6z = -30 + 56
13x - 6z = 26 (1)

2x - y + z = 6
2x - (2x + z - 14)/5 + z = 6
10x/5 + (-2x - z + 14)/5 + 5z/5 = 6
(10x - 2x - z + 14 + 5z)/5 = 6
8x + 4z + 14 = 6 × 5
8x + 4z + 14 = 30
8x + 4z = 30 - 14
8x + 4z = 16 (2)

(1) 13x - 6z = 26
(2) 8x + 4z = 16

13x - 6z = 26
13x = 6z + 26
x = (6z + 26)/13

8x + 4z = 16
8(6z + 26)/13 + 4z = 16
(48z + 208)/13 + 52z/13 = 16
48z + 52z + 208 = 16 × 13
100z + 208 = 208
100z = 208 - 208
100z = 0
z = 0/100
z = 0

13x - 6z = 26
6z = 13x - 26
z = (13x - 26)/6

8x + 4z = 16
8x + 4(13x - 26)/6 = 16
48x/6 + (52x - 104)/6 = 16
(48x + 52x - 104)/6 = 16
100x - 104 = 16 × 6
100x - 104 = 96
100x = 96 + 104
100x = 200
x = 200/100
x = 2

2x - 5y + z = 14
2x = 5y - z + 14
x = (5y - z + 14)/2

2x - y + z = 6
2(5y - z + 14)/2 - y + z = 6
5y - z + 14 - y + z = 6
4y + 14 = 6
4y = 6 - 14
4y = -8
y = -8/4
y = -2

Jadi nilai x , y , dan z adalah {2 , -2 , 0}