tentukan himpunan peny dari 2x-y+z=4 x+3y-z=-5 -x-4y+2z=7

abaikan kimia nya....

2x - y + z = 4
x + 3y - z = -5
dieliminasi

2x - y + z = 4
x + 3y - z = -5
__________ +
3x + 2y = -1 ----> (1)


2x - y + z = 4 | dikali 2
-x - 4y + 2z = 7 | dikali 1
____________ -
4x - 2y + 2z = 8
-x -4y + 2z =7
____________ -
5x + 2y = 1 ------> (2)

(1) dikali (2)

3x + 2y = -1
5x + 2y = 1
__________ -
-2x = -2
x = -2 / -2
x = 1 ----> (3)

masukan x ---> 5.1 + 2y = 1
----> 5 + 2y = 1
----> 2y = 6
----> y = 3 -------> (4)

masukan x, y
2x - y + z = 4
2.1 - 3 + z = 4
2 - 3 + z = 4
-1 + z = 4
z = 5

jadi, x = 1, y = 3, z = 5