Jawab:

x + y + z = 9

Penjelasan dengan langkah-langkah:

3x + 2y - z = 8 … I

8x - 3y + 2z = 15 … II

-2x + 5y + 3z = 23 … III

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Eliminasi I dan II:

3x + 2y - z = 8    |×2| 6x + 4y - 2z = 16

8x - 3y + 2z = 15 |×1| 8x - 3y + 2z = 15 +

                                   14x + y = 31 … IV

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Eliminasi II dan III:

8x - 3y + 2z = 15    |×3| 24x - 9y + 6z = 45

-2x + 5y + 3z = 23 |×2| -4x + 10y + 6z = 46 -

                                       28x - 19y = -1 … V

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Eliminasi IV dan V:

14x + y = 31   |×2| 28x + 2y = 62

28x - 19y = -1 |×1| 28x - 19y = -1 -

                                     21y = 63

                                         y = ⁶³⁄₂₁

                                         y = 3

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Substitusi y ke IV:

14x + y = 31

14x + 3 = 31

14x = 31 - 3

14x = 28

    x = ²⁸⁄₁₄

    x = 2

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Substitusi x dan y ke I:

     3x + 2y - z = 8

3(2) + 2(3) - z = 8

        6 + 6 - z = 8

             12 - z = 8

                   -z = 8 - 12

                   -z = -4

                    z = 4

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Nilai x + y + z:

= 2 + 3 + 4

= 5 + 4

= 9