2x + 3y + 4z= 0 X + y + z = 1 3x - 2y - 2z = 3

2x + 3y +4z = 0 ......(1)
x + y + z =1..................(2)
3x-2y-2z = 3.............(3)

eliminasi pers (1) dan (2)
2x + 3y + 4z = 0 | 1 | 2x + 3y + 4z = 0
x + y + z = 1 |2 | 2x + 2y + 2z = 2
---------------------------_
y + 2 z = -2....(4)

eliminasi pers (2) dan (3)
x + y + z = 1 |3| 3x + 3y +3z = 3
3x -2y -2z = 3 |1| 3x -2y - 2z = 3
-------------------------_
5y +5z = 0.....(5)
eliminasi pers (4) dan (5)
y + 2z = -2 |5| 5y + 10z = -10
5y+5z= 3 |1| 5y + 5z = 3
----------------------_
5z = -13
z = -13/5

y + 2z = -2
y + 2(-13/5) = -2
y + -26/5 = -2
y = -2 + 26/5
y = -10/5 +26/5
y= -16/5

x + y + z =1
x -16/5 -13/5 =1
x -29/5 = 1
x = 1 + 29/5
= 5/5 +29/5
= 34/5


bukti:

x + y + z = 1
34/5 -16/5 -13/5 = 1
5/5 = 1
1=1