himpunan penyelesaian dari sistem persaman 4x+3y-z=0 x+2y+9z=13 2x+5y-z=10 nilai dari 2x+3y+4z==

Saya Gunakan metode subtitusi ya

4x + 3y - z = 0
z = 4x + 3y

x + 2y + 9z = 13
x + 2y + 9(4x + 3y) = 13
x + 2y + 36x + 27y = 13
37x + 29y = 13
y = (13 - 37x) / 29

2x + 5y - z = 10
2x + 5(13-37x / 29) - (4x + 3y) = 10
2x + (65 - 185x)/29 - 4x - 3y = 10
(65 - 185x)/29 - 2x - 3(13-37x / 29) = 10
(65 - 185x)/29 - 2x - (39 - 111x)/29 = 10

masing² dikalikan 29
65 - 185x - 58x - 39 + 111x = 290
26 - 132x = 290
132x = 26 - 290
132x = -264
x = -2

y = (13 - 37x) / 29
y = (13 - 37(-2) / 29
y = (13 + 74) / 29
y = 87 / 29
y = 3

z = 4x + 3y
z = 4(-2) + 3(3)
z = -8 + 9
z = 1

HP {x , y , z}
HP {-2 , 3 , 1}

Hasil dari
= 2x + 3y + 4z
= 2(-2) + 3(3) + 4(1)
= -4 + 9 + 4
= 9

semoga berguna +_+