Travs T

20 November 2023 11:47

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Travs T

20 November 2023 11:47

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tentukan himpunan penyelesaian persamaan 3x + y = 5 dan 2x + 3y = 8 metode eliminasi..

tentukan himpunan penyelesaian persamaan 3x + y = 5 dan 2x + 3y = 8 metode eliminasi..

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Jawaban terverifikasi

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09 Desember 2023 08:07

Jawaban terverifikasi

<p>Jawaban yang benar adalah x = 1 dan y = 2</p><p>&nbsp;</p><p>Pembahasan :</p><p>3x + y = 5 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;(1)</p><p>2x + 3y = 8 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;(2)</p><p>&nbsp;</p><p>Eliminasi variabel y untuk mendapatkan nilai x</p><p>3x + y = 5 &nbsp; &nbsp; &nbsp; &nbsp; (dikali 3) --&gt; 9x + 3y = 15</p><p>2x + 3y = 8 &nbsp; &nbsp; &nbsp; (dikali 1) --&gt; <u>2x + 3y = 8 &nbsp;&nbsp;</u> _</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 7x &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;= 7</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;x = 1</p><p>Eliminasi variabel x untuk mendapatkan nilai y</p><p>3x + y = 5 &nbsp; &nbsp; &nbsp; &nbsp; (dikali 2) --&gt; 6x + 2y = 10</p><p>2x + 3y = 8 &nbsp; &nbsp; &nbsp; (dikali 3) --&gt; 6<u>x + 9y = 24 &nbsp;&nbsp;</u> _</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; -7y = -14</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;y = 2</p><p>Jadi, Penyelesaiannya adalah x = 1 dan y = 2</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;</p>

Jawaban yang benar adalah x = 1 dan y = 2

 

Pembahasan :

3x + y = 5              (1)

2x + 3y = 8            (2)

 

Eliminasi variabel y untuk mendapatkan nilai x

3x + y = 5         (dikali 3) --> 9x + 3y = 15

2x + 3y = 8       (dikali 1) --> 2x + 3y = 8    _

                                                      7x          = 7

                                                       x = 1

Eliminasi variabel x untuk mendapatkan nilai y

3x + y = 5         (dikali 2) --> 6x + 2y = 10

2x + 3y = 8       (dikali 3) --> 6x + 9y = 24    _

                                                              -7y = -14

                                                               y = 2

Jadi, Penyelesaiannya adalah x = 1 dan y = 2

                                                       


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