Di ketahui persamaan
x+3y-z = -2
2x+y+2z = 5
3x-2y+z=9
nilai x+y+z adalah
X + 3y – z = -2 …..pers.(1)
2x + y – 2z = 5 …..pers. (2)
3x – 2y + z = 9 …..pers.(3)
pers. (1) & (2)
x + 3y - z = -2 …………(x2) -> 2x + 6y - 2z = -4
2x + y + 2z = 5 ………….(x1) -> 2x + y + 2z = 5 (+)
4y + 7y = 1 …………..pers.(4)
pers. (1) & (3)
x + 3y - z = -2
3x - 2y + z =9 (+)
4x + y = 7 ……pers.(5)
pers. (4) & (5)
4x + 7y = 1
4x+ y = 7 (-)
6y = -6
y = -6 / 6
y = -1 ……pers.(6)
pers. (5) & (6)
4x + y = 7
4x + (-1) = 7
4x -1 =7
4x = 7 + 1
4x = 8
x = 8 / 4
x = 2 ……pers.(7)
pers. (1), (6) & (7)
x + 3y - z = -2
(2) + 3(-1) – z = -2
2 – 3 – z = -2
-1 – z = -2
-z = -2 – (-1)
-z = -2 + 1
-z = -1 …..( x -1 )
z = 1 ….pers. (8)
x + y + z = 2 + (-1) + 1
= 2
jadi, x + y + z = 2