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Nilai  yang memenuhi  adalah ...

Pertanyaan

Nilai begin mathsize 14px style open parentheses x plus y close parentheses end style yang memenuhi begin mathsize 14px style open square brackets table row cell 2 x end cell 2 row 5 1 end table close square brackets open square brackets table row 1 2 row 3 cell x minus y end cell end table close square brackets equals open square brackets table row 12 14 row 8 11 end table close square brackets end style adalah ...

  1. begin mathsize 14px style 3 end style 

  2. begin mathsize 14px style 5 end style 

  3. begin mathsize 14px style 9 end style 

  4. begin mathsize 14px style 10 end style 

  5. begin mathsize 14px style 12 end style 

Pembahasan Soal:

Diketahui:

Perkalian dua martiks ordo begin mathsize 14px style 2 cross times 2 end style, yaitu:

begin mathsize 14px style open square brackets table row cell 2 x end cell 2 row 5 1 end table close square brackets open square brackets table row 1 2 row 3 cell x minus y end cell end table close square brackets equals open square brackets table row 12 14 row 8 11 end table close square brackets end style

Operasikan bentuk matriks dengan perkalian sebagai berikut:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open square brackets table row cell 2 x end cell 2 row 5 1 end table close square brackets open square brackets table row 1 2 row 3 cell x minus y end cell end table close square brackets end cell equals cell open square brackets table row 12 14 row 8 11 end table close square brackets end cell row cell open square brackets table row cell 2 x open parentheses 1 close parentheses plus 2 open parentheses 3 close parentheses end cell cell 2 x open parentheses 2 close parentheses plus 2 open parentheses x minus y close parentheses end cell row cell 5 open parentheses 1 close parentheses plus 1 open parentheses 3 close parentheses end cell cell 5 open parentheses 2 close parentheses plus 1 open parentheses x minus y close parentheses end cell end table close square brackets end cell equals cell open square brackets table row 12 14 row 8 11 end table close square brackets end cell row cell open square brackets table row cell 2 x plus 6 end cell cell 4 x plus 2 x minus 2 y end cell row cell 5 plus 3 end cell cell 10 plus x minus y end cell end table close square brackets end cell equals cell open square brackets table row 12 14 row 8 11 end table close square brackets end cell row cell open square brackets table row cell 2 x plus 6 end cell cell 6 x minus 2 y end cell row 8 cell 10 plus x minus y end cell end table close square brackets end cell equals cell open square brackets table row 12 14 row 8 11 end table close square brackets end cell end table end style

Perhatikan bahwa pada matriks terbentuk persamaan:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 2 x plus 6 end cell equals cell 12 space space space... space open parentheses 1 close parentheses end cell row cell 6 x minus 2 y end cell equals cell 14 space space space... space open parentheses 2 close parentheses end cell end table end style

Sehingga diperoleh nilai begin mathsize 14px style x end style, yaitu:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 2 x plus 6 end cell equals 12 row cell 2 x end cell equals cell 12 minus 6 end cell row cell 2 x end cell equals 6 row x equals cell 6 over 2 end cell row x equals 3 end table end style

Kemudian substitusi begin mathsize 14px style x equals 3 end style ke persamaan ke-begin mathsize 14px style open parentheses 2 close parentheses end style, yaitu:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 6 x minus 2 y end cell equals 14 row cell 6 open parentheses 3 close parentheses minus 2 y end cell equals 14 row cell 18 minus 2 y end cell equals 14 row cell negative 2 y end cell equals cell 14 minus 18 end cell row cell negative 2 y end cell equals cell negative 4 end cell row y equals cell fraction numerator negative 4 over denominator negative 2 end fraction end cell row y equals 2 end table end style

Diperoleh nilai begin mathsize 14px style open parentheses x plus y close parentheses end style sebagai berikut:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell x plus y end cell equals cell 3 plus 2 end cell row blank equals 5 end table end style

Maka, nilai begin mathsize 14px style open parentheses x plus y close parentheses end style adalah begin mathsize 14px style 5 end style.

Jadi, jawaban yang tepat adalah B.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 04 April 2021

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