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Pertanyaan

Diketahui sistem persamaan Nilai 3x + y adalah ....

Diketahui sistem persamaan

begin mathsize 14px style open curly brackets table row cell fraction numerator 5 over denominator x minus 1 end fraction minus fraction numerator 6 over denominator x plus 4 end fraction equals 9 comma end cell row cell fraction numerator 2 over denominator x minus 1 end fraction minus fraction numerator 3 over denominator x plus 4 end fraction equals 3. end cell end table close end style

Nilai 3x + y adalah ....

  1. 0

  2. 1

  3. 2

  4. 3

  5. 4

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Jawaban terverifikasi

Jawaban

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 begin mathsize 14px style 3 x plus y equals 3 open parentheses 4 over 3 close parentheses minus 3 equals 1 end style.    

Pembahasan

Misalkan Berarti 5a - 6b = 9 2a - 3b = 3 Sehingga Jadi, .

begin mathsize 14px style fraction numerator 5 over denominator x minus 1 end fraction minus fraction numerator 6 over denominator y plus 4 end fraction equals 9 fraction numerator 2 over denominator x minus 1 end fraction minus fraction numerator 3 over denominator y plus 4 end fraction equals 3 end style

Misalkan

begin mathsize 14px style fraction numerator 1 over denominator x minus 1 end fraction equals a text  lalu end text space fraction numerator 1 over denominator y plus 4 end fraction equals b end style

Berarti

5a - 6b = 9
2a - 3b = 3

begin mathsize 14px style table row cell 5 a minus 6 b equals 9 end cell row cell 2 a minus 3 b equals 3 end cell end table open parentheses table row cell cross times 1 end cell row cell cross times 2 end cell end table close parentheses table row cell 5 a minus 6 b equals 9 end cell blank row cell bottom enclose 4 a minus 6 b equals 3 end enclose end cell minus end table 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 space space space space space space space space space space a equals 3 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 space space space space space space space space space space b equals 1 end style

Sehingga

begin mathsize 14px style fraction numerator 1 over denominator x minus 1 end fraction equals 3 x minus 1 equals 1 third x equals 1 third plus 1 equals 4 over 3  fraction numerator 1 over denominator y plus 4 end fraction equals 1 y plus 4 equals 1 y equals negative 3 end style

Jadi, begin mathsize 14px style 3 x plus y equals 3 open parentheses 4 over 3 close parentheses minus 3 equals 1 end style.    

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