Question

Sistem persamaan linear
x+2y=-3
y+2z=4
x+y+2z=5
mempunyai himpunan penyelesaian {(x,y,z)}
nilai dari 3(x+z) adalah
a.9
b.10
c.11
d.12
e.13

Answer 1

Verified answer

X + 2y = - 3
x = - 2y - 3

subtitusi ke :
x + y + 2z = 5
( - 2y - 3) + y + 2z = 5
- y + 2z = 5 + 3
- y + 2z = 8

eliminasi
- y + 2z = 8
y + 2z = 4
----------------(+)
4z = 12
z = 3

subtitusi ke :
y + 2z = 4
y + 2(3) = 4
y + 6 = 4
y = 4 - 6
y = - 2

subtitusi ke :
x + y + 2z = 5
x - 2 + 2(3) = 5
x - 2 + 6 = 5
x + 4 = 5
x = 5 - 4
x = 1

nilai 3(x + z )
= 3 ( 1 + 3)
= 3 ( 4)
= 12 ( D )