Nilai y yang memenuhi sistem persamaan: 4x+5y-2z=15 3x-2y+z=3 2x+y+3z=2

4x+5y-2z=15 ..... (1)
3x-2y+z=3 ...........(2)
2x+y+3z=2 ...........(3)

eliminasi (1) & (2)
4x+5y-2z=15 ..... (dikali 3)
3x-2y+z=3 ...........(dikali 4)
..
12x - 15y - 6z = 45
12x - 8y + 4z = 12
--------------------------- --
- 7y - 10z = 33 .........(4)

elimimasi (2) dan (3)
3x-2y+z=3 ...........( dikali 2)
2x+y+3z=2 ...........(dikali 3)
..
6x - 4y + 2z = 6
6x + 3y + 9z = 6
------------------------- --
- 7y - 7z = 0 ..........(5)

eliminasi (4) dan (5)
- 7y - 10z = 33
- 7y - 7z = 0
-------------------- --
- 3z = 33
z = 33 ÷ (-3)
z = - 11

substitusi z = - 11 ke - 7y - 10z = 33
- 7y - 10(-11) = 33
- 7y +110 = 33
- 7y = 33 - 110
- 7y = - 77
y = -77 ÷ (-7)
y = 11

subatitusi z = - 11 dan y = 11 ke 4x+5y-2z=15
4x + 5(11) - 2(-11) = 15
4x + 55 + 22 = 15
4x + 77 = 15
4x = 15 - 77
4x = - 62
x = - 62 ÷ 4
x = - 13

jadi x = - 13, y = 11, z = - 11

4x+5y-2z=15.......(1)
3x -2y+z =3..........(2)
2x+y+3z=2...........(3)

eliminasi z dari pers.(1) dan (2)
4x+5y-2z=15 |x1| 4x+5y-2z=15
3x-2y+z=3     |x2| 6x-4y+2z=6   ~~~~~10x+y=21......(4)

eliminasi z dari (2) dan (3)
3x-2y+z=3  |x3| 9x-6y+3z=9
2x+y+3z=2 |x1| 2x+t+3z  =2 ~~~~~7x-7y=7........(5)

eliminasi y dari (4) dan (5)
10x+y=21 |x7| 70x+7y=147
7x-7y=7    |x1| 7x-7y=7 ~~~~~  77x=154
                                                      x=2

substitusi pers.4
10x+y  =21
10(2)+y=21
20+y    =21
           y=21-20
           y=1