Jawaban:

x = 0, y = 0, dan z = 1

Penjelasan dengan langkah-langkah:

4x - 2y + z = 1 (1)

2y - 4z = -4 (2)

x + 5z = 5 (3)

Dari persamaan (3), diperoleh

x + 5z = 5

<=> x = 5 - 5z (4)

Substitusi persamaan (4) ke persamaan (1)

4x - 2y + z = 1

<=> 4(5 - 5z) - 2y + z = 1

<=> 20 - 20z - 2y + z = 1

<=> 20 - 19z - 2y = 1

<=> -19z - 2y = 1 - 20

<=> -19z - 2y = -19 (dibagi -1)

<=> 2y + 19z = 19 (5)

Eliminasi persamaan (2) dan persamaan (5)

2y - 4z = -4

2y + 19z = 19

__________ --

0y - 23z = -23

z = -23 / (-23)

z = 1

Substitusi nilai z = 1 ke persamaan (3)

x + 5z = 5

<=> x + 5(1) = 5

<=> x + 5 = 5

<=> x = 5 - 5

<=> x = 0

Substitusi nilai x = 0 dan z = 1 ke persamaan (1)

4x - 2y + z = 1

<=> 4(0) - 2y + 1 = 1

<=> 0 - 2y + 1 = 1

<=> -2y = 1 - 1

<=> -2y = 0

<=> y = 0