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Nilai minimum dari  yang memenuhi  adalah ...

Pertanyaan

Nilai minimum dari negative x minus 3 y yang memenuhi 2 y minus x less or equal than y plus x less or equal than 3 y comma space 2 y plus x minus 20 less or equal than 0 comma space 9 minus y minus x less or equal than 0 adalah ... 

  1. negative 35 

  2. negative 28 

  3. negative 25 

  4. negative 21 

  5. negative 15 

Pembahasan Soal:

Perhatikan bahwa 

2 y minus x less or equal than y plus x less or equal than 3 y left right double arrow 2 y minus x less or equal than y plus x space space dan space straight y plus straight x less or equal than 3 straight y space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space left right double arrow space space space space space space space y less or equal than 2 x space space space space space space space space space space space space space space space space space x less or equal than 2 y

Selanjutnya 

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 y plus x minus 20 end cell less or equal than cell 0 space left right double arrow x plus 2 y less or equal than 20 end cell row blank blank blank row cell 9 minus y minus x end cell less or equal than cell 0 space left right double arrow space x plus y greater or equal than 9 space end cell end table  

  • Menentukan titik potong garis dengan sumbu koordinat 


 
 

 

  • Uji titik  open parentheses 0 comma space 0 close parentheses 

table attributes columnalign right center left columnspacing 0px end attributes row cell x plus 2 y end cell less or equal than 20 row cell open parentheses 0 close parentheses plus 2 open parentheses 0 close parentheses end cell less or equal than 20 row 0 less or equal than 20 row blank blank cell memenuhi space end cell row blank blank blank row cell straight x plus straight y end cell greater or equal than 9 row cell open parentheses 0 close parentheses plus open parentheses 0 close parentheses end cell greater or equal than 9 row 0 greater or equal than 9 row blank blank cell tidak space memenuhi end cell end table 

  • Grafik 


 
 

  • Titik potong garis 

           titik A, perpotongan y equals 2 x space dan space x plus y equals 9

table attributes columnalign right center left columnspacing 0px end attributes row cell x plus y end cell equals 9 row cell x plus 2 x end cell equals 9 row cell 3 x end cell equals 9 row x equals 3 row blank blank blank row y equals cell 2 x end cell row blank equals cell 2 open parentheses 3 close parentheses end cell row blank equals 6 end table 

Jadi A open parentheses 3 comma space 6 close parentheses

         Titik B, perpotongan x equals 2 y space dan space x plus y equals 9 

table attributes columnalign right center left columnspacing 0px end attributes row cell x plus y end cell equals 9 row cell 2 y plus y end cell equals 9 row cell 3 y end cell equals 9 row y equals 3 row blank blank blank row x equals cell 2 y end cell row blank equals cell 2 open parentheses 3 close parentheses end cell row blank equals 6 end table 

Jadi, B open parentheses 6 comma space 3 close parentheses

         Titik C, perpotongan x equals 2 y space dan space x plus 2 y equals 20 

table attributes columnalign right center left columnspacing 0px end attributes row cell x plus 2 y end cell equals 20 row cell 2 y plus 2 y end cell equals 20 row cell 4 y end cell equals 20 row y equals 5 row blank blank blank row x equals cell 2 y end cell row blank equals cell 2 open parentheses 5 close parentheses end cell row blank equals 10 end table 

 Jadi, C open parentheses 10 comma space 5 close parentheses

      Titik D, perpotongan y equals 2 x space dan space x plus 2 y equals 20  

table attributes columnalign right center left columnspacing 0px end attributes row cell x plus 2 y end cell equals 20 row cell x plus 2 open parentheses 2 x close parentheses end cell equals 20 row cell 5 x end cell equals 20 row x equals 4 row blank blank blank row y equals cell 2 x end cell row blank equals cell 2 open parentheses 4 close parentheses end cell row blank equals 8 end table 

Jadi, D open parentheses 4 comma space 8 close parentheses 

  • Uji titik pojok 

f open parentheses x comma space y close parentheses equals negative x minus 3 y A open parentheses 3 comma space 6 close parentheses equals negative 3 minus 3 open parentheses 6 close parentheses equals negative 21 B open parentheses 6 comma space 3 close parentheses equals negative 6 minus 3 open parentheses 3 close parentheses equals negative 15 C open parentheses 10 comma space 5 close parentheses equals negative 10 minus 3 open parentheses 5 close parentheses equals negative 25 D open parentheses 4 comma space 8 close parentheses equals negative 4 minus 3 open parentheses 8 close parentheses equals negative 28  

Jadi, nilai minimum dari negative x minus 3 y adalah negative 28

Dengan demikian, jawaban yang tepat adalah B.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 19 Juli 2021

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