ZAHWA N

04 Februari 2025 14:46

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ZAHWA N

04 Februari 2025 14:46

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Jawaban terverifikasi

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Leli M

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04 Februari 2025 16:26

Jawaban terverifikasi

<p><strong>Jawaban yang tepat adalah 4</strong></p><p><strong>Pembahasan:</strong></p><p>-4x - 2y + z = 3 ...(1)</p><p>x + 3y - 2z = -1 ...(2)</p><p>2x + y - 3z = -9 ...(3)</p><p>&nbsp;</p><ul><li>Eliminasi <strong>x </strong>pada Persamaan (1) dan (2)</li></ul><p>-4x - 2y + z = 3 |x1| &nbsp;-4x - 2y + z = 3</p><p>x + 3y - 2z = -1 |x4| &nbsp;4x + 12y - 8z = -4</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; ----------------------------- &nbsp;+</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 10y -7z &nbsp;= -1 ...(4)</p><p>&nbsp;</p><ul><li>Eliminasi <strong>x </strong>pada Persamaan (2) dan (3)</li></ul><p>x + 3y - 2z = -1 |x2| &nbsp;2x + 6y - 4z = -2</p><p>2x + y - 3z = -9 |x1| &nbsp;2x + y - 3z = -9&nbsp;</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; --------------------------- –</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 5y - z = 7 ...(5)</p><p>&nbsp;</p><ul><li>Eliminasi <strong>z </strong>pada Persamaan (4) dan (5)</li></ul><p>10y - 7z = -1 &nbsp;|x1| &nbsp;10y - 7z = -1</p><p>5y - z = 7 &nbsp; &nbsp; &nbsp; &nbsp;|x7| &nbsp;35y - 7z = 49</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; --------------------- –</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; -25y &nbsp; &nbsp; &nbsp;= -50</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;y &nbsp; &nbsp; &nbsp; = -50/-25</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;<strong>y &nbsp; &nbsp; &nbsp; = 2</strong></p><p>&nbsp;</p><ul><li>Substitusi nilai <strong>y = 2 </strong>ke Persamaan (5)</li></ul><p>5y - z = 7</p><p>5(2) - z = 7</p><p>10 - z = 7</p><p>-z = 7 - 10</p><p>-z = -3</p><p><strong>z = 3</strong></p><p>&nbsp;</p><ul><li>Substitusi nilai <strong>y = 2</strong>, dan <strong>z = 3</strong> ke Persamaan (2)</li></ul><p>x + 3y - 2z = -1</p><p>x + 3(2) - 2(3) = -1</p><p>x + 6 - 6 = -1</p><p><strong>x = -1</strong></p><p>&nbsp;</p><p>x = -1, y = 2, z = 3</p><p><strong>Jadi, x + y + z = (-1) + 2 + 3 = 4</strong></p>

Jawaban yang tepat adalah 4

Pembahasan:

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

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

2x + y - 3z = -9 ...(3)

 

  • Eliminasi x pada Persamaan (1) dan (2)

-4x - 2y + z = 3 |x1|  -4x - 2y + z = 3

x + 3y - 2z = -1 |x4|  4x + 12y - 8z = -4

                                  -----------------------------  +

                                            10y -7z  = -1 ...(4)

 

  • Eliminasi x pada Persamaan (2) dan (3)

x + 3y - 2z = -1 |x2|  2x + 6y - 4z = -2

2x + y - 3z = -9 |x1|  2x + y - 3z = -9 

                                  --------------------------- –

                                          5y - z = 7 ...(5)

 

  • Eliminasi z pada Persamaan (4) dan (5)

10y - 7z = -1  |x1|  10y - 7z = -1

5y - z = 7        |x7|  35y - 7z = 49

                                --------------------- –

                                  -25y      = -50

                                       y       = -50/-25

                                       y       = 2

 

  • Substitusi nilai y = 2 ke Persamaan (5)

5y - z = 7

5(2) - z = 7

10 - z = 7

-z = 7 - 10

-z = -3

z = 3

 

  • Substitusi nilai y = 2, dan z = 3 ke Persamaan (2)

x + 3y - 2z = -1

x + 3(2) - 2(3) = -1

x + 6 - 6 = -1

x = -1

 

x = -1, y = 2, z = 3

Jadi, x + y + z = (-1) + 2 + 3 = 4


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