Melan M

15 November 2023 22:29

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Melan M

15 November 2023 22:29

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Tias T

16 November 2023 00:09

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<p>2x+y-3z=3 &nbsp; &nbsp; .....(1)<br>x-y+5z=-2 &nbsp; &nbsp; .....(2)<br>2x+2y-z=-1 &nbsp; &nbsp; .....(3)</p><ul><li><br><strong>Eliminasi x, persamaan (1) dan (2)</strong><br>2x+y-3z=3 |×1| 2x+y-3z=3<br>x-y+5z=-2 &nbsp;|×2| <u>2x-2y+10z=-4 &nbsp; &nbsp;-</u><br>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 3y-13z=7 &nbsp; &nbsp; &nbsp;.....(4)</li><li><br><strong>Eliminasi x, persamaan (1) dan (3)</strong><br>2x+y-3z=3<br><u>2x+2y-z=-1 &nbsp; &nbsp; -</u><br>&nbsp; &nbsp; -y-2z=4 &nbsp; &nbsp; &nbsp;.....(5)</li><li><br><strong>Eliminasi y, persamaan (4) dan (5)</strong><br>3y-13z=7 |×1| 3y-13z=7<br>-y-2z=4 &nbsp; &nbsp;|×3| <u>-3y-6z=12 &nbsp; &nbsp; &nbsp;+</u><br>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;-19z=19<br>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;z=-1 &nbsp; &nbsp; .....(6)</li><li><br><strong>Eliminasi z, persamaan (4) dan (5)</strong><br>3y-13z=7 |×2| 6y-26z=14<br>-y-2z=4 &nbsp; |×13| <u>-13y-26z=52 &nbsp; &nbsp; &nbsp; -</u><br>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 19y=-38<br>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;y=-2 &nbsp; &nbsp; .....(7)</li><li><br><strong>Substitusi persamaan (6) dan (7) ke persamaan (3)</strong><br>2x+2y-z=-1<br>2x+2(-2)-(-1)=-1<br>2x-4+1=-1<br>2x=-1-1+4<br>2x=2<br>x=1</li></ul><p>Jadi nilai x+y+z = 1+(-2)+(-1)<br>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = -2 &nbsp; &nbsp; &nbsp;&nbsp;<br><strong>Jawabannya C</strong></p><p><strong>:)</strong></p>

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


  • Eliminasi x, persamaan (1) dan (2)
    2x+y-3z=3 |×1| 2x+y-3z=3
    x-y+5z=-2  |×2| 2x-2y+10z=-4    -
                                    3y-13z=7      .....(4)

  • Eliminasi x, persamaan (1) dan (3)
    2x+y-3z=3
    2x+2y-z=-1     -
        -y-2z=4      .....(5)

  • Eliminasi y, persamaan (4) dan (5)
    3y-13z=7 |×1| 3y-13z=7
    -y-2z=4    |×3| -3y-6z=12      +
                                 -19z=19
                                       z=-1     .....(6)

  • Eliminasi z, persamaan (4) dan (5)
    3y-13z=7 |×2| 6y-26z=14
    -y-2z=4   |×13| -13y-26z=52       -
                              19y=-38
                                   y=-2     .....(7)

  • Substitusi persamaan (6) dan (7) ke persamaan (3)
    2x+2y-z=-1
    2x+2(-2)-(-1)=-1
    2x-4+1=-1
    2x=-1-1+4
    2x=2
    x=1

Jadi nilai x+y+z = 1+(-2)+(-1)
                            = -2       
Jawabannya C

:)


RUMI C

18 Oktober 2025 00:24

kok bisa z = -1 19 nya kalok di pindah ruas emang ngga berubah ya?

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