Khairunnisa D

30 Oktober 2023 12:59

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Khairunnisa D

30 Oktober 2023 12:59

Pertanyaan

x + 4y = 7 2x + 3y = 9 Kerjakan dengan metode a. eliminasi b. subtitusi c. campuran

x + 4y = 7
2x + 3y = 9

Kerjakan dengan metode
a. eliminasi
b. subtitusi
c. campuran

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Jawaban terverifikasi

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Sumber W

Community

30 Oktober 2023 16:30

Jawaban terverifikasi

<p>x + 4y = 7 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; (1)<br>2x + 3y = 9 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; (2)</p><p>&nbsp;</p><p>a. <strong>Metode Elimiminasi</strong></p><p>&nbsp; &nbsp;&nbsp;<strong> Eliminasi variabel x untuk mendapatkan nilai y</strong></p><p>&nbsp; &nbsp; &nbsp;x + 4y = 7 &nbsp; &nbsp;(dikali 2) ---&gt; 2x + 8y = 14<br>&nbsp; &nbsp; 2x + 3y = 9 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;---&gt; <u>2x + 3y = 9 &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; &nbsp; 5y = 5</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; &nbsp; y = 1</p><p>&nbsp; &nbsp;&nbsp;<strong>Eliminasi Variabel y untuk mendapatkan nilai x</strong></p><p>&nbsp; &nbsp; x + 4y = 7 &nbsp; &nbsp; &nbsp; (dikali 3) --&gt; 3x + 12y = 21<br>&nbsp; &nbsp; 2x + 3y = 9 &nbsp; &nbsp; (dikali 4) --&gt; <u>8x + 12y = 36&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;-5x &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;= -15</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 = 3</p><p>&nbsp; &nbsp; Himpunan Penyelesaian adalah {3,1}</p><p>&nbsp;</p><p>b. <strong>Metode Substitusi</strong></p><p>&nbsp; &nbsp; &nbsp;x + 4y = 7 --&gt; x = 7 - 4y &nbsp; &nbsp; &nbsp; &nbsp;(1)<br>&nbsp; &nbsp; &nbsp;2x + 3y = 9 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;(2)</p><p>&nbsp;</p><p>&nbsp; &nbsp;&nbsp;<strong> Substitusikan persamaan (1) Ke persamaan (2)</strong></p><p>&nbsp; &nbsp; &nbsp;2x + 3y = 9</p><p>&nbsp; &nbsp; &nbsp;2(7 - 4y) + 3y = 9</p><p>&nbsp; &nbsp; &nbsp;14 - 8y + 3y = 9</p><p>&nbsp; &nbsp; &nbsp;-5y = 9 - 14</p><p>&nbsp; &nbsp; &nbsp;-5y = -5</p><p>&nbsp; &nbsp; &nbsp; y = 1</p><p>&nbsp; &nbsp; &nbsp;<strong>Substitusikan y = 1 ke persamaan (1)</strong></p><p>&nbsp; &nbsp; &nbsp; x = 7 - 4y</p><p>&nbsp; &nbsp; &nbsp; x = 7 - 4(1)</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;= 7 - 4</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;= 3</p><p>&nbsp; &nbsp; &nbsp; &nbsp; Himpunan Penyelesaian adalah {3,1}</p><p>&nbsp;</p><p>C. <strong>Metode Campuran&nbsp;</strong></p><p><strong>&nbsp; &nbsp; &nbsp;</strong>x + 4y = 7 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; (1)<br>&nbsp; &nbsp; &nbsp;2x + 3y = 9 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; (2)</p><p><strong>&nbsp; &nbsp; &nbsp; Eliminasi variabel x untuk mendapatkan nilai y</strong></p><p>&nbsp; &nbsp; &nbsp; x + 4y = 7 &nbsp; &nbsp;(dikali 2) ---&gt; 2x + 8y = 14<br>&nbsp; &nbsp; &nbsp;2x + 3y = 9 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; ---&gt; <u>2x + 3y = 9 &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; &nbsp; 5y = 5</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; &nbsp; y = 1</p><p>&nbsp; &nbsp; &nbsp;&nbsp;<strong>Substitusikan y = 1 ke persamaan (1)</strong></p><p>&nbsp; &nbsp; &nbsp; &nbsp;<strong> </strong>x + 4y = 7&nbsp;</p><p>&nbsp; &nbsp; &nbsp; &nbsp;x + 4(1) = 7&nbsp;</p><p>&nbsp; &nbsp; &nbsp; &nbsp;x = 7 - 4</p><p>&nbsp; &nbsp; &nbsp; &nbsp;x = 3</p><p>&nbsp; &nbsp; &nbsp; &nbsp;Himpunan Penyelesaian adalah {3,1}</p>

x + 4y = 7             (1)
2x + 3y = 9           (2)

 

a. Metode Elimiminasi

     Eliminasi variabel x untuk mendapatkan nilai y

     x + 4y = 7    (dikali 2) ---> 2x + 8y = 14
    2x + 3y = 9                      ---> 2x + 3y = 9    _

                                                                5y = 5

                                                                  y = 1

    Eliminasi Variabel y untuk mendapatkan nilai x

    x + 4y = 7       (dikali 3) --> 3x + 12y = 21
    2x + 3y = 9     (dikali 4) --> 8x + 12y = 36  _

                                                       -5x            = -15

                                                        x = 3

    Himpunan Penyelesaian adalah {3,1}

 

b. Metode Substitusi

     x + 4y = 7 --> x = 7 - 4y        (1)
     2x + 3y = 9                              (2)

 

     Substitusikan persamaan (1) Ke persamaan (2)

     2x + 3y = 9

     2(7 - 4y) + 3y = 9

     14 - 8y + 3y = 9

     -5y = 9 - 14

     -5y = -5

      y = 1

     Substitusikan y = 1 ke persamaan (1)

      x = 7 - 4y

      x = 7 - 4(1)

         = 7 - 4

         = 3

        Himpunan Penyelesaian adalah {3,1}

 

C. Metode Campuran 

     x + 4y = 7             (1)
     2x + 3y = 9           (2)

      Eliminasi variabel x untuk mendapatkan nilai y

      x + 4y = 7    (dikali 2) ---> 2x + 8y = 14
     2x + 3y = 9                     ---> 2x + 3y = 9    _

                                                                5y = 5

                                                                  y = 1

      Substitusikan y = 1 ke persamaan (1)

        x + 4y = 7 

       x + 4(1) = 7 

       x = 7 - 4

       x = 3

       Himpunan Penyelesaian adalah {3,1}


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Namira N

30 Oktober 2023 13:02

<p>a.eliminasi</p>

a.eliminasi


Khairunnisa D

30 Oktober 2023 14:16

bikin jalannya satu" kak:(

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