#matematika wajibkls 10

x/3 + y/2 - z = 7
x/4 - 3y/2 + z/2 = -6
x/6 - y/4 - z/3 = 1

Tinjau persamaan i
x/3 + y/2 - z = 7 [x 6]
2x + 3y - 6z = 42 ... (i)

Tinjau persamaan ii
x/4 - 3y/2 + z/2 = -6 [x 4]
x - 6y + 2z = -24 ... (ii)

Tinjau persamaan iii
x/6 - y/4 - z/3 = 1 [x 12]
2x - 3y - 4z = 12 ... (iii)

Eliminasi persamaan (i) dan (iii)
2x + 3y - 6z = 42
2x - 3y - 4z = 12
–––––––––– (–)
6y - 2z = 30 ... (iv)

Eliminasi persamaan (i) dan (ii)
2x + 3y - 6z = 42
x - 6y + 2z = -24 |x 2|
––––––––––––– (–)
15y - 10z = 90
3y - 2z = 18 ... (v)

Eliminasi persamaan (iv) dan (v)
6y - 2z = 30
3y - 2z = 18
–––––––– (–)
3y = 12
y = 4

3(4) - 2z = 18
2z = 12 - 18
z = -6/2
z = -3

2x - 3(4) - 4(-3) = 12
2x = 12
x = 6

x - y + z = 6 - 4 - 3 = -1